# Difference between revisions of "Complexity Zoo References"

Main Zoo - Complexity Garden - Zoo Glossary - Zoo References

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

##### A

[Aar02] S. Aaronson. Quantum lower bound for the collision problem, Proceedings of ACM STOC'2002, pp. 635-642, 2002. arXiv:quant-ph/0111102.

[Aar03] S. Aaronson. Lower bounds for local search by quantum arguments, Proceedings of ACM STOC 2004. arXiv:quant-ph/0307149, ECCC TR03-057.

[Aar03b] S. Aaronson. Multilinear formulas and skepticism of quantum computing, Proceedings of ACM STOC 2004. arXiv:quant-ph/0311039, ECCC TR03-079.

[Aar04b] S. Aaronson. Limitations of quantum advice and one-way communication, Proceedings of IEEE Complexity 2004, pp. 320-332, 2004. arXiv:quant-ph/0402095, ECCC TR04-026.

[Aar05] S. Aaronson. Quantum computing and hidden variables, Physical Review A 71:032325, March 2005. arXiv:quant-ph/0408035.

[Aar05b] S. Aaronson. Quantum computing, postselection, and probabilistic polynomial-time, Proceedings of the Royal Society A, 461(2063):3473-3482, 2005. arXiv:quant-ph/0412187.

[Aar05c] S. Aaronson. NP-complete problems and physical reality. ACM SIGACT News, March 2005 quant-ph/0502072.

[Aar06] S. Aaronson. Oracles are subtle but not malicious, Proceedings of IEEE Complexity 2006, 2006. arXiv:cs.CC/0504048, ECCC TR05-040.

[Aar06b] S. Aaronson. QMA/qpoly is contained in PSPACE/poly: de-Merlinizing quantum protocols, Proceedings of IEEE Complexity 2006, 2006. arXiv:quant-ph/0510230.

[AK06] S. Aaronson and G. Kuperberg. Quantum versus classical proofs and advice, submitted, 2006. arXiv:quant-ph/0604056.

[ABFL2014] S. Aaronson, A. Bouland, J. Fitzsimons, M. Lee The space "just above" BQP arXiv:arxiv.org/abs/1412.6507

[AB00] E. Allender and D. A. M. Barrington. Uniform Circuits for Division: Consequences and Problems. J. Comput. System Sci. 65 (2002), no. 4, 695--716. ECCC TR00-65, 2000.

[ABD+08] S. Aaronson, S. Beigi, A. Drucker, et al. The power of unentanglement, Electronic Colloquium on Computational Complexity, ECCC Report TR08-051, accepted on May 02, 2008. http://eccc.hpi-web.de/eccc-reports/2008/TR08-051/index.html

[ABF+94] J. Aspnes, R. Beigel, M. L. Furst, and S. Rudich. The expressive power of voting polynomials, Combinatorica 14(2):135-148, 1994. http://www.cs.yale.edu/~aspnes/stoc91voting.ps

[ABK+02] E. Allender, H. Buhrman, M. Koucký, D. van Melkebeek, and D. Ronneburger. Power from random strings, Proceedings of IEEE FOCS'2002, pp. 669-678, 2002. ECCC TR02-028.

[ABL98] A. Ambainis, D. M. Barrington, and H. LêThanh. On counting AC0 circuits with negative constants, Proceedings of MFCS (Mathematical Foundations of Computer Science), pp. 419-427, 1998. ECCC TR98-020.

[ABO99] E. Allender, R. Beals, and M. Ogihara. The complexity of matrix rank and feasible systems of linear equations, Computational Complexity 8(2):99-126, 1999. ECCC TR96-024, DIMACS TR 97-40.

[ABV95] W. Aiello, M. Bellare, and R. Venkatesan. Knowledge on the average - perfect, statistical, and logarithmic, Proceedings of ACM STOC'95, 1995.

[ACG+99] G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation: Combinatorial optimization problems and their approximability properties, Springer-Verlag, 1999. See also "A compendium of NP optimization problems" (P. Crescenzi and V. Kann, eds.), http://www.nada.kth.se/~viggo/wwwcompendium/.

[ADH97] L. Adleman, J. DeMarrais, and M. Huang. Quantum computability, SIAM Journal on Computing 26:1524-1540, 1997.

[AFM01] L. Antuñes, L. Fortnow, and D. van Melkebeek. Computational depth, Proceedings of IEEE Complexity'01, pp. 266-273, 2001. http://people.cs.uchicago.edu/~fortnow/papers/depth.ps

[AG00] C. Alvarez and R. Greenlaw. A compendium of problems complete for symmetric logarithmic space, Journal of Computational Complexity 9:73-95, 2000. ECCC TR96-039.

[AG04] S. Aaronson and D. Gottesman. Improved Simulation of Stabilizer Circuits, Phys. Rev. A 70, 052328, 2004. arXiv:quant-ph/0406196.

[AGH90] W. Aiello, S. Goldwasser, and J. Håstad. On The Power Of Interaction. Combinatorica 10 (1990), no. 1, 3--25.

[AGK07] D. Aharonov, D. Gottesman, and J. Kempe;stad. The power of quantum systems on a line. FOCS 2007.

[Agr01] M. Agrawal. For completeness, sublogarithmic space is no space, Information Processing Letters (82), 2001-2002, iss. 6, 321-325. http://www.cse.iitk.ac.in/~manindra/isomorphism/sublog-completeness.pdf

[AJT83] M. Ajtai. Σ-1-1-Formulae on finite structures, Annals of Pure and Applied Logic (24), 1983, 1-48.

[AH87] L. Adleman and M. Huang. Recognizing primes in random polynomial time, Proceedings of ACM STOC'87, pp. 462-470, 1987.

[AH87b] W. Aiello and J. Håstad. Perfect zero-knowledge languages can be recognized in two rounds, Proceedings of IEEE FOCS 1987, pp. 439-448, 1987.

[AIK04] B. Applebaum, Y. Ishai, and E. Kushilevitz. Cryptography in NC0, Proceedings of IEEE FOCS 2004. http://www.cs.technion.ac.il/~yuvali/pubs/AIK04.ps.

[AJ93] C. Alvarez and B. Jenner. A very hard log-space counting class, Theoretical Computer Science 107:3-30, 1993.

[AK02] V. Arvind and P. Kurur. Graph isomorphism is in SPP, ECCC TR02-037, 2002.

[AK06] S. Aaronson and G. Kuperberg. Quantum Versus Classical Proofs and Advice. arXiv:quant-ph/0604056, 2006.

[AK96] F. Ablayev and M. Karpinski. On the power of randomized branching programs, Proceedings of the International Colloquium on Automata, Languages, and Programming (ICALP), Springer-Verlag 1099, pp. 348-356, 1996. ECCC TR95-054, DIMACS TR 96-46.

[AKL+79] R. Aleliunas, R. M. Karp, R. J. Lipton, L. Lovász, and C. Rackoff. Random walks, traversal sequences, and the complexity of maze problems, Proceedings of IEEE FOCS'79, pp. 218-223, 1979.

[AKR+03] E. Allender, M. Koucký, D. Ronneburger, et al. Derandomization and distinguishing complexity, Proceedings of the 18th Annual IEEE Conference on Computational Complexity, 209-220.

[AKS94] V. Arvind, J. Köbler and R. Schuler. On helping and interactive proof systems, Algorithms and Computation: 5th International Symposium, 137-145.

[AKS02] M. Agrawal, N. Kayal, and N. Saxena. Primes is in P, Annals of Mathematics, 160 (2004), 781-793. http://www.cse.iitk.ac.in/primality.pdf.

[AKS+95] V. Arvind, J. Köbler, U. Schöning, and R. Schuler. If NP has polynomial-size circuits, then MA=AM, Theoretical Computer Science 137, 1995. http://www.informatik.hu-berlin.de/Institut/struktur/algorithmenII/Papers/ma-am.ps.gz

[All96] E. Allender. Circuit complexity before the dawn of the new millennium, Proceedings of the 16th Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FST&TCS), Lecture Notes in Computer Science 1180, pp. 1-18, 1996. DIMACS TR 97-49.

[All99] E. Allender. The permanent requires large uniform threshold circuits, Chicago Journal of Theoretical Computer Science 7, 1999. DIMACS TR 97-51.

[ALM+98] S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and hardness of approximation problems, Journal of the ACM 45(3):501-555, 1998. ECCC TR98-008.

[AM04] R. Alur and P. Madhusudan. Visibly Pushdown Languages, Proceedings of ACM STOC'04, 2004., 202-211.

[AM09] R. Alur and P. Madhusudan. Adding Nesting Structure to Words., Journal of the ACM 56(3), Article 16, May 2009.

[AMP02] F. Ablayev, C. Moore, and C. Pollett. Quantum and stochastic branching programs of bounded width, Proceedings of the International Colloquium on Automata, Languages, and Programming (ICALP), 2002. arXiv:quant-ph/0201139, ECCC TR02-013.

[AMS06] N. Alon, D. Moshkovitz, and S. Safra. Algorithmic construction of sets for k-restrictions, ACM Transactions on Algorithms (TALG) 2(2): 153–177, 2006. doi:10.1145/1150334.1150336

[AN02] D. Aharonov and T. Naveh. Quantum NP - a survey, arXiv:quant-ph/0210077.

[AP95] G. Ausiello and M. Protasi Local search, reducibility, and approximability of NP optimization problems, Information Processing Letters 54:73-79, 1995.

[AR01] M. Alekhnovich and A. A. Razborov. Resolution is not automatizable unless W[P] is tractable, Proceedings of IEEE FOCS'01, pp. 210-219, 2001.

[AR03] D. Aharonov and O. Regev. A lattice problem in quantum NP, arXiv:quant-ph/0307220.

[AR88] E. Allender and R. Rubinstein. P-printable sets, SIAM Journal on Computing 17(6):1193-1202, 1988.

[AR16] B. Applebaum and P. Raykov. From Private Simultaneous Messages to Zero-Information Arthur-Merlin Protocols and Back, Proceedings of TCC(A2), pp. 65-82, 2016.

[Aro96] S. Arora. Polynomial time approximation scheme for Euclidean TSP and other geometric problems, Proceedings of IEEE FOCS'96, pp. 2-11, 1996. http://www.cs.princeton.edu/~arora/pubs/tsp1.ps

[ARZ99] E. Allender, K. Reinhardt, and S. Zhou. Isolation, matching, and counting: uniform and nonuniform upper bounds, Journal of Computer and System Sciences 59:164-181, 1999. http://www.cs.rutgers.edu/pub/allender/matching.pdf.

[AS94] E. Allender and M. Strauss. Measure on small complexity classes with applications for BPP, Proceedings of IEEE FOCS'94, pp. 807-818, 1994. ECCC TR94-004, DIMACS TR 94-18.

[AS98] S. Arora and M. Safra. Probabilistic checking of proofs: a new characterization of NP, Journal of the ACM 45(1):70-122, 1998. http://www.cs.princeton.edu/~arora/pubs/as.ps.

[ASV00] A. Ambainis, L. Schulman, and U. Vazirani. Quantum computing with highly mixed states, Proceedings of ACM STOC'2000, pp. 705-714, 2000. arXiv:quant-ph/0003136.

[ATW+00] R. Armoni, A. Ta-Shma, A. Wigderson, and S. Zhou. An O(log(n)4/3) algorithm for (s,t) connectivity in undirected graphs, Journal of the ACM 47(2):294-311, 2000. http://whiteboard.cs.tau.ac.il/~amnon/Papers/ATWZ.jacm00.pdf

[AV04] V. Arvind and T. C. Vijayaraghavan. Abelian permutation group problems and logspace counting classes, Proceedings of the 19th IEEE Conference on Computational Complexity, .

[AW90] E. Allender and K. W. Wagner. Counting hierarchies: polynomial time and constant depth circuits, Bulletin of the EATCS 40, February 1990. http://people.cs.uchicago.edu/~fortnow/beatcs/column40.ps.

##### B

[Bab85] L. Babai. Trading Group Theory for Randomness. In 17th STOC, pages 421--429, 1985.

[Bab87] L. Babai. Random oracles separate PSPACE from the polynomial-time hierarchy. Information Processing Letters, 26 (1987) 51-53.

[Bar02] B. Barak. A probabilistic-time hierarchy theorem for "slightly non-uniform" algorithms, Proceedings of RANDOM'2002, 2002. http://www.math.weizmann.ac.il/~/boaz/Papers/bptime.ps

[Bar89] D. A. M. Barrington. Bounded-width polynomial-size branching programs can recognize exactly those languages in NC1, Journal of Computer and System Sciences 38:150-164, 1989.

[Baz95] C. Bazgan. Approximation de problèmes d'optimisation et de fonctions totales de NP, PhD thesis, INRIA, Orsay, France, 1998. http://l1.lamsade.dauphine.fr/~bazgan/Papers/these.ps

[BB12] M. Bläser and B. Manthey. Smoothed Complexity Theory, Proceedings of the 37th Int. Symp. on Mathematical Foundations of Computer Science, 2012. ArXiv: 1202.1936.

[BB92] A. Berthiaume and G. Brassard. The quantum challenge to structural complexity theory. Proceedings of Structure in Complexity Theory, 1992, 132--137.

[BBB+97] C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani. Strengths and weaknesses of quantum computing, SIAM Journal on Computing, 26(5):1510-1523, 1997. arXiv:quant-ph/9701001.

[BBF98] R. Beigel, H. Buhrman, and L. Fortnow. NP might not be as easy as detecting unique solutions, Proceedings of ACM STOC'98, pp. 203-208, 1998. http://people.cs.uchicago.edu/~fortnow/papers/newiso.ps.

[BBR94] D. A. M. Barrington, R. Beigel, and S. Rudich. Representing Boolean functions as polynomials modulo composite integers, Computational Complexity, 4:367-382, 1994. http://www.cis.temple.edu/~beigel/papers/bbr-mods-cc.html.

[BBS86] J. Balcázar, R. Book, and U. Schöning. Sparse sets, lowness, and highness, SIAM Journal on Computing 15:739-747, 1986.

[BCE+95] P. Beame, S. Cook, J. Edmonds, R. Impagliazzo, and T. Pitassi. The relative complexity of NP search problems, Proceedings of ACM STOC'95, pp. 303-314, 1995. http://www.cs.washington.edu/homes/beame/search.ps

[BCH86] P. Beame, S. Cook, and J. Hoover. Log depth circuits for division and related problems, SIAM Journal on Computing 15:994-1003, 1986 http://www.cs.washington.edu/homes/beame/papers/division.ps.

[BCG+92] S. Ben-David, B. Chor, O. Goldreich, and M. Luby. On the theory of average case complexity, Journal of Computer and System Sciences 44(2):193-219, 1992. http://www.cs.technion.ac.il/~shai/aver.pdf

[BCS+97] L. Blum, F. Cucker, M. Shub, and S. Smale. Complexity and Real Computation, Springer-Verlag, 1997.

[BCD+89] A. Borodin, S. A. Cook, P. W. Dymond, W. L. Ruzzo, and M. L. Tompa. Two applications of inductive counting for complementation problems, SIAM Journal on Computing 18:559-578, 1989.

[BCP83] A. Borodin, S. A. Cook, and N. Pippenger. Parallel computations for well-endowed rings and space-bounded probabilistic machines, Information and Control 58:113-136, 1983.

[BD99] H. Buhrman and W. van Dam. Bounded quantum query complexity, Proceedings of IEEE Complexity'99, pp. 149-156, 1999. arXiv:quant-ph/9903035.

[BDG88] J. L. Balcázar, J. Díaz, and J. Gabarró Structural complexity 1

[BDH+92] G. Buntrock, C. Damm, U. Hertrampf, and Ch. Meinel. Structure and importance of logspace-MOD-classes, Mathematical Systems Theory 25:223-237, 1992. http://www.num.math.uni-goettingen.de/damm/papers/BDHM92.ps.gz.

[Bei89] R. Beigel. On the relativized power of additional accepting paths, Proceedings of IEEE Complexity'89, pp. 216-224, 1989. http://www.cis.temple.edu/~beigel/papers/ukp-structures.PS.gz.

[Bei94] R. Beigel. Perceptrons, PP, and the polynomial hierarchy, Computational Complexity 4:339-349, 1994. http://www.cis.temple.edu/~beigel/papers/delta2p-cc.PS.gz.

[Ber80] L. Berman. The complexity of logical theories, Theoretical Computer Science 11:71-78, 1980.

[BF92] R. Beigel and J. Feigenbaum. On Being Incoherent Without Being Very Hard. Comput. Complexity 2 (1992), no. 1, 1--17 http://www.cis.temple.edu/~beigel/papers/bf-coherent-cc.html

[BF99] H. Buhrman and L. Fortnow. One-sided versus two-sided randomness, Proceedings of the 16th Symposium on Theoretical Aspects of Computer Science (STACS), pp. 100-109, 1999. http://people.cs.uchicago.edu/~fortnow/papers/rpvsbpp.ps.

[BF03] R. Beigel. Are Cook and Karp ever the same?, Proceedings of the 18th Annual IEEE Conference on Computational Complexity, 333-336.

[BFL91] L. Babai, L. Fortnow, and C. Lund. Nondeterministic exponential time has two-prover interactive protocols, Computational Complexity 1:3-40, 1991. http://people.cs.uchicago.edu/~fortnow/papers/mip2.ps.

[BFM88] M. Blum, P. Feldman, and S. Micali. Non-interactive zero-knowledge proofs and their applications, Proceedings of the 20th STOC, ACM, 1988.

[BFS86] L. Babai, P. Frankl, and J. Simon. Complexity classes in communication complexity theory, Proceedings of IEEE FOCS'86, pp. 337-347, 1986.

[BFT98] H. Buhrman, L. Fortnow, and T. Thierauf. Nonrelativizing separations, Proceedings of IEEE Complexity'98, pp. 8-12, 1998. http://people.cs.uchicago.edu/~fortnow/papers/nonrel.ps.

[BGS75] T. Baker, J. Gill, and R. Solovay. Relativizations of the P=?NP question, SIAM Journal on Computing 4:431-442, 1975.

[BH77] L. Berman and J. Hartmanis. On isomorphism and density of NP and other complete sets, SIAM Journal on Computing 6:305-322, 1977.

[BG03] M. Ben-Or and D. Gutfreund. Trading help for interaction in statistical zero-knowledge proofs, J. Cryptology 16 (2003), no. 2, 95--116. http://www.cs.huji.ac.il/~danig/pubs/help_interaction.ps

[BG69] R. Book and S. Greibach. Quasi-realtime languages, Proceedings of ACM STOC pp. 15-18, 1969. http://portal.acm.org/citation.cfm?id=800169.805416

[BG81] C. H. Bennett and J. Gill. Relative to a random oracle A, PA != NPA != coNPA with probability 1, SIAM Journal on Computing, 10(1):96-113, 1981. DOI:10.1137/0210008

[BG92] R. Beigel and J. Gill. Counting classes: thresholds, parity, mods, and fewness, Theoretical Computer Science 103(1):3-23, 1992. http://www.cis.temple.edu/~beigel/papers/bg-mods-tcs.PS.gz.

[BG98] R. Beigel and J. Goldsmith. Downward separation fails catastrophically for limited nondeterminism classes, SIAM Journal on Computing 17(5):1420-1429, 1998. http://www.cis.temple.edu/~beigel/papers/bg-beta-draft.PS.gz.

[BG94] M. Bellare and S. Goldwasser. The complexity of decision versus search, SIAM Journal on Computing 23(1):91-119, 1994. http://www.cs.ucsd.edu/users/mihir/papers/compip.pdf

[BGG+90] M. Ben-Or, O. Goldreich, S. Goldwasser, J. Håstad, J. Kilian, S. Micali, and P. Rogaway. Everything provable is provable in zero-knowledge, Advances in Cryptology: CRYPTO'88 (S. Goldwasser, ed.), Lecture Notes in Computer Science 403, Springer-Verlag, pp. 37-56, 1990.

[BGK+88] M. Ben-Or, S. Goldwasser, J. Kilian, and A. Wigderson. Multi-prover interactive proofs: how to remove intractability, Proceedings of ACM STOC'88, pp. 113-131, 1988.

[BG82] A. Blass and Y. Gurevich. On the unique satisfiability problem, Information and Control 55(1-3):80-88, 1982.

[BGM02] E. Böhler, C. Glaßer, and D. Meister. Error-bounded probabilistic computations between MA and AM, Mathematical foundations of computer science 2003, 249--258. http://haegar.informatik.uni-wuerzburg.de/users/glasser/publications/sbp-ma-am-tr.pdf

[BGR93] B. von Braunmühl, R. Gengler, and R. Rettinger. The alternation hierarchy for sublogarithmic space is infinite, Computational Complexity, v.3 n.3, p.207-230, July 1993 [doi>10.1007/BF01271368] [1]

[BH91] S. R. Buss and L. Hay. On truth-table reducibility to SAT, Information and Computation 91(1):86-102, 1991.

[BH97] C. Berg and J. Håstad. On the BPP hierarchy problem, Technical Report TRITA-NA-9702, Royal Institute of Technology, Sweden, 1997. ftp://ftp.nada.kth.se/pub/documents/Theory/Christer-Berg/bpp.ps.

[BH08] H. Buhrman and J. Hitchcock. NP-Hard sets are exponentially eense unless NP is contained in coNP/poly, Electronic Colloquium on Computational Complexity, ECCC Report TR08-022, accepted on Mar 11, 2008. http://eccc.hpi-web.de/eccc-reports/2008/TR08-022/index.html

[BHR00] B. Borchert, L. Hemaspaandra, and J. Rothe. Restrictive Acceptance Suffices for Equivalence Problems. LMS J. Comput. Math. 3 (2000), 86--95 arXiv:cs.CC/9907041.

[BHW89] R. Beigel, L. Hemachandra, and G. Wechsung. On the power of probabilistic polynomial time, Proceedings of IEEE Complexity'89, pp. 225-230, 1989.

[BHZ87] R. B. Boppana, J. Håstad, and S. Zachos. Does co-NP have short interactive proofs?, Information Processing Letters 25:127-132, 1987.

[BK89] M. Blum and S. Kannan. Designing programs that check their work, Proceedings of ACM STOC'89, 1989.

[BKL+00] D. A. M. Barrington, P. Kadau, K.-J. Lange, and P. McKenzie. On the complexity of some problems on groups input as multiplication tables, http://www-fs.informatik.uni-tuebingen.de/~lange/Arbeiten/fologlog/bklm/neu.ps.gz Proceedings of IEEE Complexity'2000, 2000.

[BKS95] R. Beigel, M. Kummer, and F. Stephan. Approximable sets, Information and Computation 120(2):304-314, 1995. http://www.cis.temple.edu/~beigel/papers/bks-queries2-ic.PS.gz.

[BLM+98] D. A. M. Barrington, C.-J. Lu, P. B. Miltersen, and S. Skyum. Searching constant width mazes captures the AC0 hierarchy, Proceedings of the 1998 Symposium of Theoretical Aspects of Computer Science (STACS'98), 1998. ECCC TR97-044.

[BLM+99] D. A. M. Barrington, C.-J. Lu, P. B. Miltersen, and S. Skyum. On monotone planar circuits, Proceedings of IEEE Complexity'99, 1999. http://www.brics.dk/~bromille/Papers/mpc.ps

[BLS84] R. Book, T. Long, and A. Selman. Quantitative relativizations of complexity classes, SIAM Journal on Computing 13(3):461-487, 1984.

[Blu67] M. Blum. A Machine-Independent Theory of the Complexity of Recursive Functions. J. ACM 14: 322-336, 1967.

[BM04] J. Buresh-Oppenheim and T. Morioka. Relativized NP search problems and propositional proof systems, Proceedings of IEEE Complexity 2004, pp. 54-67, 2004. ECCC TR03-084.

[BM88] L. Babai and S. Moran. Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity classes, Journal of Computer and Systems Sciences 36:254-276, 1988.

[Boo72] R. Book. On languages accepted in polynomial time, SIAM Journal on Computing 1(4):281-287, 1972.

[Boo74] R. Book. Comparing complexity classes, Journal of Computer and System Sciences 3(9):213-229, 1974.

[Boo94] R. Book. On collapsing the polynomial-time hierarchy, Information Processing Letters 52(5):235-237, 1994.

[Bor77] A. Borodin. On relating time and space to size and depth, SIAM Journal on Computing 6:733-744, 1977.

[Bra77] F.-J. Brandenburg. On one-way auxiliary pushdown automata, Proceedings of the Third GI-Conference on Theoretical Computer Science, Springer LNCS vol. 48, pp. 132-144, 1977.

[Bra79] G. Brassard. A note on the complexity of cryptography IEEE Transactions on Information Theory, 25(2):232-233, 1979.

[Bra06] S. Bravyi. Efficient algorithm for a quantum analogue of 2-SAT, arXiv:quant-ph/0602108v1, 2006.

[BRS91] R. Beigel, N. Reingold, and D. A. Spielman. PP is closed under intersection, Proceedings of ACM STOC'91, pp. 1-9, 1991. http://www.cis.temple.edu/~beigel/papers/brs-pp-jcss.PS.gz.

[Bru90] J. Bruck. Harmonic analysis of polynomial threshold functions, SIAM J. Discrete Math., 3 (1990) 168-177.

[BS00] B. Borchert and F. Stephan. Looking for an Analogue of Rice's Theorem in Circuit Complexity Theory. MLQ Math. Log. Q. 46 (2000), no. 4, 489--504 http://math.uni-heidelberg.de/logic/bb/papers/Rice.ps

[BS90] J. Bruck and R. Smolensky. Polynomial threshold functions, AC0 functions and spectral norms, Proceedings of IEEE FOCS'90, pp. 632-641, 1990.

[BS90b] R. B. Boppana and M. Sipser. The complexity of finite functions. chapter in Handbook of Theoretical Computer Science, Volume A (J. van Leeuwen, editor), Elsevier, 1990.

[BSF02] A. Ben-Hur, H. T. Siegelmann, and S. Fishman. A theory of complexity for continuous time systems, Journal of Complexity 18(1):51-86, 2002. http://cmgm.stanford.edu/~asab/Papers/dds2.ps.gz

[BT04] H. Buhrman and L. Torenvliet. Separating complexity classes using structural properties, Proceedings of IEEE Complexity 2004, pp. 130-138, 2004. http://staff.science.uva.nl/~leen/PAPERS/superrobustsets.pdf

[BT06] A. Bogdanov and L. Trevisan. Average-Case Complexity, ECCC Report TR06-073, Revision 01, accepted on Fri Sep 29 22:13:11 2006.

[BT88] D. A. M. Barrington and D. Thérien. Finite monoids and the fine structure of NC1, Journal of the ACM 35(4):941-952, 1988.

[Bur00] P. Bürgisser. Completeness and Reduction in Algebraic Complexity Theory, Springer Series in Algorithms and Computation in Mathematics, Volume 7, 2000.

[Buss93] S. Buss. Algorithms for Boolean formula evaluation and for tree-contraction, Proof Theory, Complexity, and Arithmetic, P. Clote and J. Krajicek (eds), Oxford University Press, 1993, pp. 95-115. http://math.ucsd.edu/~sbuss/ResearchWeb/Boolean3/index.html

[BV97] E. Bernstein and U. Vazirani. Quantum complexity theory, SIAM Journal on Computing, 26(5):1411-1473, 1997. http://www.cs.berkeley.edu/~vazirani/bv.ps

[BVW98] R. Book, H. Vollmer, and K. W. Wagner. Probabilistic type-2 operators and "almost"-classes, Computational Complexity 7(3):265-289, 1998.

[BVW07] H. Burhman, N. Vereshchajin, R. de Wolf. On computation and communication with small bias. Proceedings of IEEE Conference on Computational Complexity 2007 24-32, 2007.

[BW03] H. Buhrman and R. de Wolf. Quantum Zero-Error Algorithms Cannot be Composed, Information Processing Letters, 87(2):79-84, 2003. arXiv:quant-ph/0211029.

##### C

[Cai01] J.-Y. Cai. S2P is contained in ZPPNP, Proceedings of IEEE FOCS'2001, pp. 620-629, 2001.

[Cai86] J.-Y. Cai. With probability one, a random oracle separates PSPACE from the polynomial hierarchy, Proceedings of ACM STOC'86, pp. 21-29, 1986.

[Cai87] J. Cai. Probability one separation of the Boolean hieararchy, Lecture Notes in Computer Science, vol 247, p148-158, 1987.

[Can96] R. Canetti. More on BPP and the polynomial-time hierarchy, Information Processing Letters 57:237-241, 1996.

[CC93] L. Cai and J. Chen. On fixed-parameter tractability and approximability of NP-hard optimization problems, Proceedings of ISTCS'93 - Israel Symposium on Theory of Computing and Systems, pp. 118-126, 1993.

[CC97] L. Cai and J. Chen. On fixed-parameter tractability and approximability of NP optimization problems, Journal of Computer and System Sciences 54(3):465-474, 1997.

[CCD+03] A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman. Exponential algorithmic speedup by quantum walk, Proceedings of ACM Symposium on Theory of Computing, pp. 59-68, 2003. arXiv:quant-ph/0209131.

[CCG+94] R. Chang, B. Chor, O. Goldreich, J. Hartmanis, J. Håstad, D. Ranjan, and P. Rohatgi. The random oracle hypothesis is false, Journal of Computer and System Sciences 49(1):24-39, 1994.

[CCH+01] J.-Y. Cai, V. Chakaravarthy, L. Hemaspaandra, and M. Ogihara. Some Karp-Lipton-type theorems based on S2, University of Rochester Computer Science Technical Report TR-759, November 2001.

[CD05] X. Chen and X. Deng 3-NASH is PPAD-Complete, online: http://eccc.uni-trier.de/eccc-reports/2005/TR05-134/Paper.pdf, nov. 2005.

[CDL01] A. Chiu, G. Davida, and B. Litow. Division in logspace-uniform NC1, Theoretical Informatics and Applications 35(3):259, 2001.

[CF91] J.-Y. Cai and M. Furst. PSPACE survives constant-width bottlenecks, International Journal of Foundations of Computer Science 2(1):67-76, 1991.

[CP07] Y. Chen and J. Flum. On parameterized path and chordless path problems, Proceedings of the IEEE Conference on Computational Complexity 2007, 250-263.

[CFL83] A. Chandra, S. Fortune, R. Lipton. Unbounded fan-in circuits and associative functions, Proceedings of the fifteenth annual ACM symposium on Theory of computing, 52-60, 1983.

[CFL+93] A. Condon, J. Feigenbaum, C. Lund, and P. Shor. Probabilistically checkable debate systems and approximation algorithms for PSPACE-hard functions (extended abstract), Proceedings of ACM STOC'93, pp. 305-314, 1993.

[CGH+88] J.-Y. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The Boolean hierarchy I: structural properties, SIAM Journal on Computing 17:1232-1252, 1988. Part II: applications in 18:95-111, 1989.

[CGR+04] M. Crasmaru, C. Glaßer, K. W. Regan, and S. Sengupta. A protocol for serializing unique strategies, submitted, 2004. http://www.cse.buffalo.edu/faculty/regan/papers/ps/CGRS03.ps.

[CH89] J.-Y. Cai and L. A. Hemachandra. On the power of parity polynomial time, Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS), Lecture Notes in Computer Science 349, pp. 229-240, Springer, 1989.

[CHT+04] R. Cleve, P. Høyer, B. Toner, and J. Watrous. Consequences and limits of nonlocal strategies, Proceedings of IEEE Complexity, pp. 236-249, 2004. arXiv:quant-ph/0404076.

[Chu41] A. Church. The calculi of lambda-conversion, Annals of Mathematical Studies 6, Princeton Univ. Press, 1941.

[CIK+03] C. Calabro, R. Impagliazzo, V. Kabanets, et al. The complexity of Unique $k$-SAT: An isolation lemma for $k$-CNFs., Proceedings of the IEEE Conference on Computational Complexity 2003, 135-141.

[CKK+95] F. Cucker, M. Karpinski, P. Koiran, T. Lickteig, and K. Werther. On real Turing machines that toss coins, Proceedings of ACM STOC'95, pp. 335-342, 1995.

[CKS81] A. K. Chandra, D. C. Kozen, and L. J. Stockmeyer. Alternation, Journal of the ACM 28:114-133, 1981.

[CKS+99] P. Crescenzi, V. Kann, R. Silvestri, and L. Trevisan. Structure in approximation classes, SIAM Journal on Computing 28:1759-1782, 1999. ECCC TR96-066.

[CKSU05] H. Cohn, R. Kleinberg, B. Szegedy, and C. Umans. Group-theoretic Algorithms for Matrix Multiplication. Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS) 379-388, 2005.

[CM01] M. Cryan and P. B. Miltersen. On pseudorandom generators in NC0, Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science (MFCS), pp. 272-284, 2001.

[CMTV98] H. Caussinus, P. McKenzie, D. Thérien, and H. Vollmer. Nondeterministic NC1 computation, Journal of Computer and System Sciences, 200-212, 1998.

[CMI00] Clay Mathematics Institute. The P versus NP problem (a millennium prize problem), with official problem description by S. Cook, http://www.claymath.org/prizeproblems/pvsnp.htm, 2000.

[CNS99] J.-Y. Cai, A. P. Nerurkar, and D. Sivakumar. Hardness and hierarchy theorems for probabilistic quasi-polynomial time, Proceedings of ACM STOC'99, pp. 726-735, 1999.

[Cob64] A. Cobham. The intrinsic computational difficulty of functions, Proceedings of the 1964 Congress on Logic, Mathematics and the Methodology of Science, pp. 24-30, 1964.

[Cob66] A. Cobham. The recognition problem for the set of perfect squares, Proceedings of the 7th Symposium on Switching and Automata Theory, pp. 78-87, 1966.

[Con73] R. Constable. Type 2 computational complexity, Proceedings of ACM STOC'73, pp. 108­-121, 1973.

[Con92] A. Condon. The complexity of stochastic games, Information and Computation 96(2):203-224, 1992.

[Coo71] S. A. Cook. The complexity of theorem-proving procedures, Proceedings of ACM STOC'71, pp. 151-158, 1971.

[Coo71b] S. A. Cook. Characterizations of pushdown machines in terms of time-bounded computers, Journal of the ACM 18(1):4-18, 1971.

[Coo79] S. A. Cook. Deterministic CFL's are accepted simultaneously in polynomial time and log squared space, Proceedings of ACM STOC'79, pp. 338-345, 1979.

[Coo85] S. A. Cook. A taxonomy of problems with fast parallel algorithms, Information and Control 64:2-22, 1985.

[CP95] P. Crescenzi and C. Papadimitriou. Reversible simulation of space-bounded computations, Theoretical Computer Science 143:159-165, 1995.

[CP07] R. Chang and S. Purini. Bounded queries and the NP Machine Hypothesis., Proceedings of the IEEE Conference on Computational Complexity 2007, 52-59.

[CR96] S. Chaudhuri and J. Radhakrishnan. Deterministic Restrictions in Circuit Complexity, Proceedings of ACM STOC 1996, pp. 30-36, 1996.

[CR06] V. Chakaravarthy and S. Roy. Oblivious symmetric alternation, Proceedings of the 23rd Symposium on Theoretical Aspects of Computer Science (STACS) 2006, 230-241. [2]

[CS92] J. Castro and C. Seara. Characterizations of some complexity classes between Θ2p and Δ2p, Proceedings of STACS 1992, pp. 305-317, 1992.

[CT94] P. Crescenzi and L. Trevisan. An approximation scheme preserving reducibility and its applications, Proceedings of 14th Annual Conference on Foundations of Software Technology and Theoretical Computer Computer Science (FSTTCS), pp. 330-341, Lecture Notes in Computer Science 880, Springer-Verlag, 1994.

[CT97] M. Cesati and L. Trevisan. On the efficiency of polynomial time approximation schemes, ECCC TR97-001, 1997.

[CT07] X. Chen and S.-H. Teng. Paths beyond local search: A nearly tight bound for randomized fixed-point computation. FOCS 2007.

[CW82] D. Coppersmith and S. Winograd. On the Asymptotic Complexity of Matrix Multiplication. SIAM J. Comput. 11(3): 472-492,1982.

[CW90] D. Coppersmith and S. Winograd. Matrix multiplication via arithmetic progressions, Journal of Symbolic Computation, 9:251–280, 1990.

[CW00] R. Cleve and J. Watrous. Fast parallel circuits for the quantum Fourier transform, Proceedings of IEEE Focs'2000, pp. 526-536, 2000. arXiv:quant-ph/0006004.

##### D

[Dam90] C. Damm. Problems complete for L, Information Processing Letters 36:247-250, 1990.

[DC89] P. W. Dymond and S. Cook. Complexity theory of parallel time and hardware, Information and Computation 80:205-226, 1989.

[DDP+98] A. De Santis, G. Di Crescenzo, G. Persiano, and M. Yung. Image density is complete for non-interactive SZK, Proceedings of the 25th International Colloquium on Automata, Languages, and Programming (ICALP), Lecture Notes in Computer Science, pp. 784-795, 1998. (Note: Some results in the paper were later retracted.)

[Dek76] M. I. Dekhtyar. On the relativization of deterministic and nondeterministic complexity classes, Mathematical Foundations of Computer Science, pp. 255-259, Springer LNCS 45, 1976.

[DF97] R. G. Downey and M. R. Fellows. Threshold dominating sets and an improved characterization of W[2], Theoretical Computer Science 189, 1997.

[DF99] R. G. Downey and M. R. Fellows. Parameterized Complexity, Springer-Verlag Monographs in Computer Science, 1999.

[DFT96] R. G. Downey, M. R. Fellows, and U. Taylor. On the parameteric complexity of relational database queries and a sharper characterization of W[1], Combinatorics, Complexity, and Logic, Proceedings of DMTCS'96, Springer-Verlag, pp. 194-213, 1996.

[DGP05] C. Daskalakis, P. W. Goldberg, and C. H. Papadimitriou The Complexity of Computing a Nash Equilibrium, online: ppad.ps, sep. 2005.

[DHI02] W. van Dam, S. Hallgren, and L. Ip. Quantum algorithms for hidden shift problems, arXiv:quant-ph/0211140, 2002.

[DP05] C. Daskalakis and C. H. Papadimitriou The Complexity of Computing a Nash Equilibrium, online: 3players.pdf, nov. 2005.

[DP08] M. David and T. Pitassi. Separating NOF communication complexity classes RP and NP, Electronic Colloquium on Computational Complexity, ECCC Report TR08-014, accepted on Feb 28, 2008.

[DW86] E. Dahlhaus and M. K. Warmuth. Membership for growing context-sensitive grammars is polynomial, Journal of Computer and System Sciences 33:456-472, 1986.

##### E

[Edm65] J. Edmonds. Paths, trees, and flowers, Canadian Journal of Mathematics 17(3):449-467, 1965.

[EY07] K. Etessami and M. Yannakakis. On the Complexity of Nash Equilibria and Other Fixed Points. Unpublished.

Paths, trees, and flowers, Canadian Journal of Mathematics 17(3):449-467, 1965.

##### F

[Fag73] R. Fagin. Contributions to the Model Theory of Finite Strucutres, Ph.D. Thesis (1973), U.C. Berkeley

[Fag74] R. Fagin. Generalized first-order spectra and polynomial-time recognizable sets, Complexity of Computation (R. M. Karp, ed.), SIAM-AMS Proceedings Vol. 7, 1974.

[Fen02] S. Fenner. PP-lowness and a simple definition of AWPP, Theory Comput. Syst. 36 (2003), no. 2, 199--212. ECCC TR02-036.

[FF..] S. Fenner, L. Fortnow, Unpublished.

[FFK+93] S. Fenner, L. Fortnow, S. Kurtz, and L. Li. An oracle builder's toolkit, Proceedings of Structure in Complexity Theory, pages 120-131, 1993. http://people.cs.uchicago.edu/~fortnow/papers/obt.ps.

[FFK94] S. Fenner, L. Fortnow, and S. Kurtz. Gap-definable counting classes, Journal of Computer and System Sciences 48(1):116-148, 1994. http://people.cs.uchicago.edu/~fortnow/papers/gaps.ps.

[FG02] J. Flum and M. Grohe. The parameterized complexity of counting problems, Proceedings of IEEE FOCS'2002, 2002.

[FGH+98] S. Fenner, F. Green, S. Homer, and R. Pruim. Quantum NP is hard for PH, Proceedings of the Sixth Italian Conference on Theoretical Computer Science, World-Scientific, pp. 241-252, 1998. arXiv:quant-ph/9812056.

[FGL+91] U. Feige, S. Goldwasser, L. Lovász, S. Safra, and M. Szegedy. Approximating clique is almost NP-complete, Proceedings of IEEE FOCS'91, pp. 2-12, 1991.

[FGM+89] M. Furer, O. Goldreich, Y. Mansour, M. Sipser, and S. Zachos. On Completeness and Soundness in Interactive Proof Systems. In Advances in Computing Research: a research annual, Vol.~5 (Randomness and Computation, S. Micali, ed.), pages 429--442, 1989.

[Fie98] U. Feige. A threshold of ln(n) for approximating set cover. Journal of the ACM (JACM), 45(4): 634--652, 1998. doi:10.1145/285055.285059

[FK05] L. Fortnow and A. Klivans. NP with small advice, Proceedings of IEEE Complexity'2005, pp. 228-234, 2005. http://people.cs.uchicago.edu/~fortnow/papers/fk.ps.

[FK97] U. Feige and J. Kilian. Limited versus polynomial nondeterminism, Chicago Journal of Theoretical Computer Science Article 1, 1997.

[FK97b] U. Feige and J. Kilian. Making games short, Proceedings of ACM STOC'1997, pp. 506-516, 1997.

[For94] L. Fortnow. The role of relativization in complexity theory, Bulletin of the EATCS 52, February 1994. http://people.cs.uchicago.edu/~fortnow/papers/relative.ps.

[For02] J. Forster. A linear lower bound on the unbounded error probabilistic communication complexity, Journal of Computer and System Sciences 65(4):612-625, 2002.

[FR74] M. J. Fischer and M. O. Rabin. Super-exponential complexity of Presburger arithmetic, Complexity of Computation (R. M. Karp, ed.), SIAM-AMS Symposium on Applied Mathematics, 1974.

[FR98] L. Fortnow and J. D. Rogers. Complexity limitations on quantum computation, Proceedings of IEEE Complexity'98, pp. 202-209, 1998. arXiv:cs.CC/9811023.

[Fri57] R. M. Friedberg. Two recursively enumerable sets of incomparable degrees of unsolvability, Proceedings of the National Academy of Sciences, 43:236-238, 1957. http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=528418&blobtype=pdf.

[FRS88] L. Fortnow, J. Rompel, and M. Sipser. On the power of multiprover interactive protocols, Proceedings of IEEE Complexity'88, 1988. http://people.cs.uchicago.edu/~fortnow/papers/mip.ps.

[FS04] L. Fortnow and R. Santhanam. Hierarchy theorems for probabilistic polynomial time, Proceedings of IEEE FOCS'2004, 2004. http://people.cs.uchicago.edu/~fortnow/papers/probhier.ps.

[FS88] L. Fortnow and M. Sipser. Are there interactive protocols for co-NP languages? Inform. Process. Lett. 28 (1988), no. 5, 249--251. http://cs-www.uchicago.edu/~fortnow/papers/conpipl.ps

[FSS84] M. Furst, J. Saxe, and M. Sipser. Parity, circuits, and the polynomial hierarchy, Mathematical Systems Theory 17:13-27, 1984.

[Fur07] M. Furer. Fast Integer Multiplication, STOC, 2007.

[FV93] T. Feder and M. Y. Vardi. Monotone monadic SNP and constraint satisfaction, Proceedings of the 25th ACM Symposium on Theory of Computing, pp. 612-622, 1993. DOI:10.1145/167088.167245.

##### G

[Gas02] W. Gasarch. The P=?NP poll, SIGACT News Complexity Theory Column 36 (L. A. Hemaspaandra, ed.), 2002.

[Geff91] V. Geffert. Nondeterministic computations in sublogarithmic space and space constructibility, SIAM Journal on Computing v. 20 iss. 3, 1991. [3]

[GG66] S. Ginsburg and S. Greibach. Deterministic context free languages, Information and Control 9:620-648, 1966.

[GGK03] W. Gasarch, E. Golub, and C. Kruskal. Constant time parallel sorting: an empirical view, J. Comput. Syst. Sci. 67:63-91, 2003.

[GHJ+91] J. Goldsmith, L. A. Hemaspaandra, D. Joseph, and P. Young. Near-testable sets. SIAM J. Comput. 20 (1991), no. 3, 506--523

[GHP00] F. Green, S. Homer, and C. Pollett. On the complexity of quantum ACC, Proceeedings of IEEE Complexity'2000, pp. 250-262, 2000. See also: F. Green, S. Homer, C. Moore, and S. Pollett. Counting, fanout, and the complexity of quantum ACC, arXiv:quant-ph/0106017, 2001.

[Gil77] J. Gill. Computational complexity of probabilistic Turing machines, SIAM Journal on Computing 6(4):675-695, 1977.

[GJ79] M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, 1979.

[GK14] S. Gharibian, and J. Kempe. Hardness of approximation for quantum problems, Quantum Information & Computation 14(5 & 6): 517-540, 2014. Extended abstract appeared in Proceeedings of the 39th International Colloquium on Automata, Languages, and Programming (ICALP), pages 387-398, Springer, 2012.

[GKR+95] F. Green, J. Köbler, K. W. Regan, T. Schwentick, and J. Torán. The power of the middle bit of a #P function, Journal of Computer and System Sciences 50(3):456-467, 1995.

[GL14] D. Gavinsky and S. Lovett. En route to the log-rank conjecture: New reductions and equivalent formulations, Proceedings of ICALP'14, pp. 514-524, 2014.

[GLM96] J. Goldsmith, M. A. Levy, and M. Mundhenk. Limited nondeterminism, SIGACT News 27(2):20-29, 1996. http://cs.engr.uky.edu/~goldsmit/papers/extended.ps

[GLM+15] M. Göös, S. Lovett, R. Meka, T. Watson, and D. Zuckerman. Rectangles Are Nonnegative Juntas, Proceedings of ACM STOC'15, pp. 257-266, 2015.

[GMR89] S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems, SIAM Journal on Computing 18(1):186-208, 1989.

[GMW91] O. Goldreich, S. Micali, and A. Wigderson. Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems, Journal of the ACM 38(1):691-729, 1991.

[GN13] D. Gosset and D. Nagaj. Quantum 3-SAT is QMA1-complete, arXiv:[4], 2013.

[GO95] A. Gajentaan and M. Overmars. On a class of $O(n^2)$ problems in computational geometry, Computational Geometry, Volume 5, Issue 3, October 1995, pages 165-185.

[Gol97] O. Goldreich. Notes on Levin's theory of average-case complexity, ECCC TR97-058.

[GP01] F. Green and R. Pruim. Relativized separation of EQP from P^NP, Information Processing Letters 80 (2001) 257-260. http://cs.clarku.edu/~fgreen/papers/eqp.ps

[GP86] L. Goldschlager and I. Parberry. On the construction of parallel computers from various bases of Boolean functions, Theoretical Computer Science 43(1):43-58, 1986.

[GP91] O. Goldreich and E. Petrank. Quantifying knowledge complexity, Proceedings of IEEE FOCS'91, pp. 59-68, 1991. http://www.wisdom.weizmann.ac.il/~oded/PS/gp.ps

[GPW15] M. Göös, T. Pitassi, and T. Watson. Deterministic Communication vs. Partition Number, Proceedings of IEEE FOCS'15, 1077-1088, 2015.

[GPW16a] M. Göös, T. Pitassi, and T. Watson. Zero-Information Protocols and Unambiguity in Arthur-Merlin Communication, Algorithmica, Online First, 2016.

[GPW16b] M. Göös, T. Pitassi, and T. Watson. The Landscape of Communication Complexity Classes, Proceedings of ICALP'16, to appear, 2016.

[Grä92] E. Grädel Capturing complexity classes b fragments of second order logic Information and computaiton 119 (1995), 129-135

[Gre90] F. Green. An oracle separating +P from PPPH, Inform. Process. Lett. 37 (1991), no. 3, 149--153.

[Gre93] F. Green. On the power of deterministic reductions to C=P, Math. Systems Theory 26 (1993), no. 2, 215--233.

[GS86] S. Goldwasser and M. Sipser. Private coins versus public coins in interactive proof systems, Proceedings of ACM STOC'86, pp. 58-68, 1986.

[GS88] J. Grollman and A. L. Selman. Complexity measures for public-key cryptosystems, SIAM Journal on Computing 17:309-335, 1988.

[GS89] Y. Gurevich and S. Shelah. Nearly Linear Time, Proceedings of LFCS'89, Springer LNCS 363, pp. 108-118, 1989.

[GS90] M. Grigni and M. Sipser. Monotone complexity, Proceedings of LMS Workshop on Boolean Function Complexity (M. S. Paterson, ed.), Durham, Cambridge University Press, 1990. http://www.mathcs.emory.edu/~mic/papers/4.ps

[GS91] M. Grigni and M. Sipser. Monotone separation of NC1 from logspace, Proceedings of IEEE Complexity'91, pp. 294-298, 1991.

[GS15] S. Gharibian, and J. Sikora. Ground state connectivity of local Hamiltonians, Proceeedings of the 42nd International Colloquium on Automata, Languages, and Programming (ICALP), volume 9134 of Lecture Notes in Computer Science, pages 617-628, 2015.

[Gri01] M. Grigni. A Sperner lemma complete for PPA, Information Processing Letters 77:5-6 (2001), pp. 255-259.

[GSS+03] C. Glaßer, A. L. Selman, S. Sengupta, and L. Zhang. Disjoint NP-pairs, ECCC TR03-011, 2003.

[GST03] D. Gutfreund, R. Shaltiel, and A. Ta-Shma. Uniform hardness vs. randomness tradeoffs for Arthur-Merlin games, Comput. Complexity 12 (2003), no. 3-4, 85--130. http://www.cs.huji.ac.il/~danig/pubs/ccc.ps.

[GSV99] O. Goldreich, A. Sahai, and S. Vadhan. Can statistical zero knowledge be made non-interactive? or on the relationship of SZK and NISZK, ECCC TR99-013, 1999. Abstract appeared in CRYPTO'99.

[GTW+91] R. Gavaldá, L. Torenvliet, O. Watanabe, and J. Balcázar. Generalized Kolmogorov complexity in relativized separations, Proceedings of MFCS'91 (Mathematical Foundations of Computer Science), Springer-Verlag Lecture Notes in Computer Science, vol. 452, pp. 269-276, 1991.

[Gup95] S. Gupta. Closure properties and witness reduction, Journal of Computer and System Sciences 50(3):412-432, 1995. ftp://ftp.cis.ohio-state.edu/pub/tech-report/1993/TR46.ps.gz

[Gur87] Y. Gurevich. Complete and incomplete randomized NP problems, Proceedings of IEEE FOCS'87, pp. 111-117, 1987.

[Gur89] E. Gurari. An Introduction to the Theory of Computation, Computer Science Press, 1989. http://www.cse.ohio-state.edu/~gurari/theory-bk/theory-bk.html.

[Gut05] G. Gutoski. Upper bounds for quantum interactive proofs with competing provers, Proceedings of IEEE Complexity'2005, pp. 334-343, 2005. http://www.cs.uwaterloo.ca/~gmgutosk/gutoskig_competing.pdf.

[GV02] M. de Graaf and P. Valiant. Comparing EQP and MODp^kP using polynomial degree lower bounds, arXiv:quant-ph/0211179, 2002.

[GV99] O. Goldreich and S. Vadhan. Comparing entropies in statistical zero-knowledge with applications to the structure of SZK, Proceedings of IEEE Complexity'99, pp. 54-73, 1999. ECCC TR98-063.

[GW05] G. Gutoski and J. Watrous. Quantum interactive proofs with competing provers, Proceedings of STACS'2005, pp. 605-616, Springer-Verlag, 2005. arXiv:cs.CC/0412102.

[GW07] G. Gutoski and J. Watrous. Toward a general theory of quantum games, In Proceedings of the 39th ACM Symposium on Theory of Computing (STOC'07), pages 565-574, 2007. arXiv:quant-ph/0611234.

[GW10] G. Gutoski and X. Wu. Short quantum games characterize PSPACE, 2010. arXiv:arXiv:1011.2787.

[GW96] A. Gál and A. Wigderson. Boolean complexity classes vs. their arithmetic analogs, Random Structures and Algorithms 9:1-13, 1996. ECCC TR95-049.

[GW14] M. Göös and T. Watson. Communication Complexity of Set-Disjointness for All Probabilities, Proceedings of RANDOM'14, 721-736, 2014.

[GZ97] O. Goldreich and D. Zuckerman. Another proof that BPP subseteq PH (and more), ECCC TR97-045.

##### H

[Hal02] S. Hallgren. Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem, Proceedings of ACM STOC'2002, 2002. http://www.cse.psu.edu/~hallgren/pell.pdf.

[Har78] J. Hartmanis. Feasible Computations and Provable Complexity Properties, SIAM, 1978.

[Har87] J. Hartmanis. The collapsing hierarchies, Bulletin of the EATCS 33, October 1987. http://external.nj.nec.com/homepages/fortnow/beatcs/column33.ps.

[Har87b] J. Hartmanis. Sparse complete sets for NP and the optimal collapse of the polynomial hierarchy, Bulletin of the EATCS 32, June 1987. http://external.nj.nec.com/homepages/fortnow/beatcs/column32.ps.

[Has87] J. Håstad. Computational Limitations for Small-Depth Circuits, MIT Press, 1987.

[Has88] J. Håstad. Oneway permutations in NC0, Information Processing Letters 26:153-155, 1988.

[Has90] J. Håstad. Tensor rank is NP-complete, J. Algorithms, 11(4):644-654, 1990.

[Has01] J. Håstad. Some optimal inapproximability results, Journal of the ACM, 48(4):798-3859, 2001. http://www-sunos4.nada.kth.se/~johanh/optimalinap.ps

[HCC+92] J. Hartmanis, R. Chang, S. Chari, D. Ranjan, and P. Rohatgi. Relativization: a revisionistic retrospective, Bulletin of the EATCS 47, June 1992. http://external.nj.nec.com/homepages/fortnow/beatcs/column47.ps.

[HCK+88] J. Hartmanis, R. Chang, J. Kadin, and S. G. Mitchell. Some observations about relativization of space bounded computations, Bulletin of the EATCS 35, June 1988. http://external.nj.nec.com/homepages/fortnow/beatcs/column35.ps.

[Hel84a] H. Heller. Relativized polynomial hierarchies extending two levels, Mathematical Systems Theory 17(2):71-84, 1984.

[Hel84b] H. Heller. On Relativized Polynomial and Exponential Computations, SIAM Journal on Computing 13(4):717-725, 1984.

[Hel86] H. Heller. On Relativized Exponential and Probabilistic Complexity Classes, Inform. and Control 71 (1986), no. 3, 231--243

[Hem89] L. Hemachandra. The strong exponential hierarchy collapses, Journal of Computer and System Sciences 39(3):299-322, 1989.

[Her90] U. Hertrampf. Relations among MOD-classes, Theoretical Computer Science 74:325-328, 1990.

[Her97] U. Hertrampf. Acceptance by transformation monoids (with an application to local self-reductions), Proceedings of IEEE Complexity'97, pp. 213-224, 1997.

[Hes01] W. Hesse. Division is in uniform TC0, Proceedings of the International Colloquium on Automata, Languages, and Programming (ICALP), 2001. http://www.cs.umass.edu/~whesse/div.ps

[HH76] J. Hartmanis and J. Hopcroft. Independence results in computer science, ACM SIGACT News 8(4):13-24, 1976.

[HH86] J. Hartmanis and L. Hemachandra. Complexity classes without machines: on complete languages for UP, Proceedings of ICALP'86, Springer-Verlag Lecture Notes in Computer Science volume 226, pp. 123-135, 1986.

[HHH98] E. Hemaspaandra, L. Hemaspaandra, and H. Hempel. What's up with downward collapse: using the easy-hard technique to link Boolean and polynomial hierarchy collapses, SIGACT News 29(3):10-22, 1998. arXiv:cs.CC/9910002.

[HHK+05] L. Hemaspaandra, C. Homan, S. Kosub, and K. Wagner. The complexity of computing the size of an interval, Technical Report TR-856, Department of Computer Science, University of Rochester, 2005. This is an expanded version of HKW01

[HHN+95] L. Hemaspaandra, A. Hoene, A. Naik, M. Ogihara, A. Selman, T. Thierauf, and J. Wang. Nondeterministically selective sets, International Journal of Foundations of Computer Science (IJFCS), 6(4):403-416, 1995.

[HHR97] E. Hemaspaandra, L. Hemaspaandra, and J. Rothe. Exact analysis of Dodgson elections: Lewis Carroll's 1876 voting system is complete for parallel access to NP, Proceedings of ICALP'97, Springer-Verlag Lecture Notes in Computer Science, 1997. arXiv:cs.CC/9907036.

[HHT97] Y. Han, L. Hemaspaandra, and T. Thierauf. Threshold computation and cryptographic security, SIAM Journal on Computing 26(1):59-78, 1997.

[HI02] W. Hesse and N. Immerman. Complete problems for dynamic complexity classes, Proceedings of Logic in Computer Science (LICS), 2002. http://www.cs.umass.edu/~immerman/pub/completeLICS.pdf

[HJV93] L. Hemaspaandra, R. Jain, and N. K. Vereshchagin. Banishing robust Turing completeness, International Journal of Foundations of Computer Science, 3-4:245-265, 1993.

[HKW01] L. Hemaspaandra, S. Kosub, and K. Wagner. The complexity of computing the size of an interval, Proceedings of ICALP'01, Springer-Verlag Lecture Notes in Computer Science, 2001.

[HLS65] J. Hartmanis, P. L. Lewis II, and R. E. Stearns. Hierarchies of memory-limited computations, Proceedings of the 6th Annual IEEE Symposium on Switching Circuit Theory and Logic Design, pp. 179-190, 1965.

[HM13] A. W. Harrow and A. Montanaro. Testing product states, quantum Merlin-Arthur games and tensor optimisation, Journal of the ACM vol. 60 no. 1, 2013

[HMP+93] A. Hajnal, W. Maass, P. Pudlák, M. Szegedy, and G. Turán. Threshold circuits of bounded depth, Journal of Computer and System Sciences 46(2):129-154, 1993.

[HN06] D. Harnik and M. Naor. On the compressibility of NP instances and cryptographic applications. Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), 719-728, 2006. http://www.cs.technion.ac.il/~harnik/Compress.pdf

[HNO+96] L. Hemaspaandra, A. Naik, M. Ogihara, and A. Selman. Computing solutions uniquely collapses the polynomial hierarchy, SIAM Journal on Computing 25(4):697-708, 1996. ECCC TR96-027.

[HO02] L. Hemaspaandra and M. Ogihara. The Complexity Theory Companion, Springer-Verlag, 2002. See also http://www.cs.rochester.edu/u/lane/=companion/.

[HPV77] J. Hopcroft, W. Paul, and L. Valiant. On time versus space, Journal of the ACM 24(2):332-337, 1977.

[HR90] B. Halstenberg and R. Reischuk. Relations between communication complexity classes, Journal of Computer and System Sciences 41(3):402-429, 1990.

[HRV00] U. Hertrampf, S. Reith, and H. Vollmer. A note on closure properties of logspace MOD classes, Information Processing Letters 75(3):91-93, 2000. http://www.thi.uni-hannover.de/forschung/publikationen/daten/he-re-vo99.ps.gz

[HS65] J. Hartmanis and R. E. Stearns. On the computational complexity of algorithms, Transactions of the AMS 117:285-305, 1965.

[HS92] S. Homer and A. L. Selman. Oracles for structural properties: the isomorphism problem and public-key cryptography, Journal of Computer and System Sciences 44(2):287-301, 1992.

[HT03] C. M. Homan and M. Thakur. One-way permutations and self-witnessing languages, Journal of Computer and System Sciences 67 (2003), 608-622. [5].

[HT06] L. Hella and J. M. Turull-Torres. Computing queries with higher-order logics, Theorical. Comput. Sci. 355 (2006), 197-214. [6].

[HY84] J. Hartmanis and Y. Yesha. Computation times of NP sets of different densities, Theoretical Computer Science 34:17-32, 1984.

##### I

[Iba72] O. Ibarra. A note concerning nondeterministic tape complexities, Journal of the ACM 4:608-612, 1972.

[IKW01] R. Impagliazzo, V. Kabanets, and A. Wigderson. In search of an easy witness: exponential time vs. probabilistic polynomial time, Proceedings of IEEE Complexity'2001, 2001. http://www.cs.sfu.ca/~kabanets/papers/exp_journal.ps.gz

[IL90] R. Impagliazzo and L. A. Levin. No better ways to generate hard NP instances than picking uniformly at random, Proceedings of IEEE FOCS'90, pp. 812-821, 1990.

[IM03] R. Impagliazzo and P. Moser. A zero one law for RP, Proceedings of the 18th Conference on Computational Complexity, 48-52. IEEE Computer Society Press, 2003.

[Imp95] R. Impagliazzo. A personal view of average-case complexity, Proceedings of the 10th Conference on Structure in Complexity Theory, 134-147. IEEE Computer Society Press, 1995.

[Imm82] N. Immerman. Relational queries computable in in polynomial time. 14th ACM STOC Symp. (1987), 86-104

[Imm83] N. Immerman. Languages That Capture Complexity Classes 15th ACM STOC Symp. (1983), 347-354 [7]

[Imm88] N. Immerman. Nondeterministic space is closed under complement, SIAM Journal on Computing, 17:935-938, 1988.

[Imm89] N. Immerman. Expressibility and Parallel Complexity SIAM Journal on Computing, 18:625-638, 1989. [8]

[Imm98] N. Immerman. Descriptive Complexity, Springer Graduate Texts in Computer Science, 1998.

[Imp02] R. Impagliazzo. Hardness as randomness: a survey of universal derandomization, Proceedings of the ICM, Beijing, vol. 3, pp. 649-658, 2002. arXiv:cs.CC/0304040.

[IN96] R. Impagliazzo and M. Naor. Efficient cryptographic schemes provably as secure as subset sum, Journal of Cryptology 9(4):199-216, 1996. http://www.wisdom.weizmann.ac.il/~naor/PAPERS/subset.ps.gz

[IPZ01] R. Impagliazzo, R. Paturi, and F. Zane. Which problems have strongly exponential complexity, Journal of Computer and System Sciences 63(4):512-530, 2001. http://cm.bell-labs.com/cm/ms/who/francis/papers/focs98-subexp.pdf.

[IS91] R. Impagliazzo and M. Sudan. Private communication, cited in [#bg94" style="color:maroon">[BG94], 1991.

[IT89] R. Impagliazzo and G. Tardos. Decision versus search problems in super-polynomial time, in Proceedings of IEEE FOCS 1989, pp. 222-227, 1989.

[IV12] T. Ito and T. Vidick. A multi-prover interactive proof for NEXP sound against entangled provers, to appear in Proceedings of IEEE FOCS 2012 arXiv:1207.0550.

[IW97] R. Impagliazzo and A. Wigderson. P=BPP if E requires exponential circuits: derandomizing the XOR lemma, Proceedings of ACM STOC'97, pp. 220-229, 1997.

##### J

[Jeř07] E. Jeřábek. Approximate counting in bounded arithmetic, Journal of Symbolic Logic 72(3):959–993, 2007.

[Jeř12] E. Jeřábek. Integer factoring and modular square roots, http://arxiv.org/abs/1207.5220

[JJUW09] R. Jain, Z. Ji, S. Upadhyay, and J. Watrous. QIP = PSPACE, arXiv:0907.4737, 2009.

[JKS02] J. C. Jackson, A. R. Klivans, and R. A. Servedio. Learnability beyond AC0, Proceedings of ACM STOC'2002, pp. 776-784, 2002.

[JL95] D. W. Juedes and J. H. Lutz. The complexity and distribution of hard problems, SIAM Journal on Computing 24(2):279-295, 1995. http://www.cs.iastate.edu/~lutz/%3DPAPERS/cdhp.ps

[Joh90] D. S. Johnson. A catalog of complexity classes, chapter 2 in Handbook of Theoretical Computer Science, Volume A (J. van Leeuwen, editor), Elsevier, 1990.

[Jon98] N. D. Jones. Logspace and Ptime Characteried by Programming Languages, [9]

[JPY88] D. S. Johnson, C. H. Papadimitriou, and M. Yannakakis. How easy is local search?, Journal of Computer and System Sciences 37:79-100, 1988.

[JSV01] M. Jerrum, A. Sinclair, and E. Vigoda. A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries, Proceedings of ACM STOC'2001, pp. 712-721, 2001. ECCC TR00-079.

[Jun85] H. Jung. On probabilistic time and space, Proceedings of 12th International Colloquium on Automata, Languages, and Programming (ICALP), Lecture Notes in Computer Science, 194:310-317, 1985.

[JW04] M. Jerrum and U. Wagner. Counting, Sampling, and Integrating: Algorithms and Complexity, Chapter 3 (lecture notes labeled as under construction). http://www.dcs.ed.ac.uk/home/mrj/ETHbook/chap3.ps.

[JW09] R. Jain and J. Watrous. Parallel approximation of non-interactive zero-sum quantum games, Proceedings of the 24th Annual IEEE Conference on Computational Complexity, pages 243–253, 2009. arXiv:0808.2775 [quant-ph].

[JWB03] D. Janzing, P. Wocjan, and T. Beth. Cooling and low energy state preparation for 3-local Hamiltonians are FQMA-complete, arXiv:quant-ph/0303186, 2003.

[JY88] D. S. Johnson and M. Yannakakis. On generating all maximal independent sets, Information Processing Letters 27(3):119-123, 1988.

##### K

[Kad88] J. Kadin. The polynomial time hierarchy collapses if the Boolean hierarchy collapses, SIAM Journal on Computing 17:1263-1282, 1988.

[Kan82] R. Kannan. Circuit-size lower bounds and non-reducibility to sparse sets, Information and Control 55:40-56, 1982.

[Kar72] R. M. Karp. Reducibility among combinatorial problems, Complexity of Computer Computations (J. W. Thatcher and R. E. Miller, eds.), Plenum Press, 1972.

[Kar86] H. Karloff. A Las Vegas algorithm for maximum matching, Combinatorica 6:387-392, 1986.

[KF84] C. M. R. Kintala and P. Fischer. Refining nondeterminism in relativized complexity classes, SIAM Journal on Computing 13:329-337, 1984.

[Kha79] L. G. Khachiyan. A polynomial algorithm for linear programming, Soviet Math Doklady 20:191-194, 1979.

[Kha93] M. Kharitonov. Cryptographic hardness of distribution-specific learning, Proceedings of ACM STOC'93, pp. 372-381, 1993.

[KI02] V. Kabanets and R. Impagliazzo. Derandomizing polynomial identity tests means proving circuit lower bounds, ECCC TR02-055, 2002.

[KKR04] J. Kempe, A. Kitaev, and O. Regev. The Complexity of the Local Hamiltonian Problem, SIAM Journal of Computing, Vol. 35(5), p. 1070-1097 (2006). arXiv:quant-ph/0406180.

[KL82] R. M. Karp and R. J. Lipton. Turing machines that take advice, Enseign. Math. 28:191-201, 1982.

[Kla03] H. Klauck. Rectangle size bounds and threshold covers in communication complexity, Proceedings of IEEE CCC'03, pp. 118-134, 2003.

[Kla07] H. Klauck. Lower bounds for quantum communication complexity, SIAM Journal on Computing 37(1):20-46, 2007.

[Kle71] S. C. Kleene. Introduction to Metamathematics, Elsevier, 1971.

[KM02] H. Kobayashi and K. Matsumoto. Quantum multi-prover interactive proof systems with limited prior entanglement, Proceedings of ISAAC'2002, pp. 115-127, 2002. arXiv:cs.CC/0102013.

[KM92] D. Koller and N. Megiddo. On the Complexity of Two-person Zero-sum Games in Extensive Form, Games and Economic Behavior 4, 528-552, 1992. http://theory.stanford.edu/~megiddo/pdf/recall.pdf

[KM99] A. Klivans and D. van Melkebeek. Graph nonisomorphism has subexponential size proofs unless the polynomial hierarchy collapses, in Proceedings of ACM STOC'99, pp. 659-667, 1999.

[KMS+99] S. Khanna, R. Motwani, M. Sudan, and U. Vazirani. On syntactic versus computational views of approximability, SIAM Journal on Computing 28:164-191, 1999. ECCC TR95-023.

[KMSY14] G. Kol, S. Moran, A. Shpilka, and A. Yehudayoff. Approximate nonnegative rank is equivalent to the smooth rectangle bound, Proceedings of the ICALP'14, pp. 701-712, 2014.

[KMY01] H. Kobayashi, K. Matsumoto, and T. Yamakami. Quantum certificate verification: single versus multiple quantum certificates, arXiv:quant-ph/0110006, 2001.

[Ko82] K. Ko. Some observations on the probabilistic algorithms and NP-hard problems, Information Processing Letters 14(1):39-43, 1982.

[Ko85] K. Ko. On some natural complete operators, Theoretical Computer Science 37(1):1-30, 1985.

[Kob02] H. Kobayashi. Non-interactive quantum statistical and perfect zero-knowledge, arXiv:quant-ph/0207158, 2002.

[Kob89] J. Köbler. Strukturelle Komplexität von Anzahlproblemen, PhD thesis, Universität Stuttgart, 1989.

[Koi96] P. Koiran. Hilbert's Nullstellensatz is in the polynomial hierarchy, Journal of Complexity 12(4):273-286, 1996, DIMACS TR 96-27.

[Koz92] D. C. Kozen. On the Myhill-Nerode theorem for trees, Bulletin of the EATCS 47:170-173, 1992.

[Koz97] D. C. Kozen. Automata and Computability, Springer-Verlag, 1997.

[KP89] J. Krajicek and P. Pudlak. Propositional Proof Systems, the Consistency of First Order Theories and the Complexity of Computations, J. Symb. Log., 54:1063-79, 1989.

[KR03] J. Kempe and O. Regev. 3-Local Hamiltonian is QMA-complete, Quantum Inf. Comput., 3(3):258-264, 2003. arXiv:quant-ph/0302079.

[Kra..] H. Krawczyk. Unpublished.

[KRC00] V. Kabanets, C. Rackoff, and S. A. Cook. Efficiently approximable real-valued functions, ECCC TR00-034, 2000.

[Kre88] M. Krentel. The complexity of optimization problems, Journal of Computer and System Sciences 36:490-509, 1988.

[KRS90] C. P. Kruskal, L. Rudolph, and M. Snir. A complexity theory of efficient parallel algorithms, Theoretical Computer Science 71:95-132, 1990.

[KS05] N. Kayal and N. Saxena. On the ring isomorphism and automorphism problems, Proceedings of the 20th Annual IEEE Conference on Computational Complexity, 2-12, 2005.

[KST+89] J. Köbler, U. Schöning, and J. Torán. On counting and approximation, Acta Informatica 26:363-379, 1989.

[KST+89b] J. Köbler, U. Schöning, S. Toda, and J. Torán. Turing machines with few accepting computations and low sets for PP, Proceedings of IEEE Complexity'89, pp. 208-215, 1989. http://www.informatik.hu-berlin.de/Forschung_Lehre/algorithmenII/Papers/few.ps.gz

[KST92] J. Köbler, U. Schöning, and J. Torán. Graph isomorphism is low for PP, Computational Complexity 2:301-330, 1992.

[KST93] J. Köbler, U. Schöning, and J. Torán. The Graph Isomorphism Problem: Its Structural Complexity, Birkhäuser, 1993.

[KSV02] A. Kitaev, A. Shen, and M. N. Vyalyi. Classical and Quantum Computation, American Mathematical Society, 2002.

[KT94] P. G. Koliatis and M. N. Thakur. Logical definability of NP optimization problems, Information and Computation 115:321-353, 1994.

[KT96] J. Köbler and S. Toda. On the power of generalized MOD-classes, Mathematical Systems Theory 29(1):33-46, 1996. ftp://theorie.informatik.uni-ulm.de/pub/papers/ti/mod.ps.gz

[Kup09] G. Kuperberg. How hard is it to approximate the Jones polynomial?, 2009. arXiv:quant-ph/0908.0512v1.

[Kur64] S. Y. Kuroda. Classes of languages and linear-bounded automata, Information and Control 7:207-233, 1964.

[Kur83] S. Kurtz. On the random oracle hypothesis, Information and Control 57:40-47, 1983.

[Kur85] S. Kurtz. On Relativized Exponential and Probabilistic Complexity Classes, Information and Control 71:231-243, 1985.

[KUW86] R. Karp, E. Upfal, and A. Wigderson. Constructing a perfect matching is in random NC, Combinatorica 6:35-48, 1986.

[KV88] M. Karpinski and R. Verbeek. Randomness, provability, and the separation of Monte Carlo time and space, Lecture Notes in Computer Science 270, pp. 189-207, Springer, 1988.

[KV94] M. Kearns and L. Valiant. Cryptographic limitations on learning Boolean formulae and finite automata, Journal of the ACM 41(1):67-95, 1994. http://www.cis.upenn.edu/~mkearns/papers/crypto.pdf

[KV96] M. Karpinski and R. Verbeek. On Randomized Versus Deterministic Computation, Theoret. Comput. Sci. 154 (1996), no. 1, 23--39. ECCC TR95-021.

[KW..] A. Kitaev and J. Watrous. Unpublished.

[KW00] A. Kitaev and J. Watrous. Parallelization, amplification, and exponential time simulation of quantum interactive proof systems, Proceedings of ACM STOC'2000, pp. 608-617, 2000. https://cs.uwaterloo.ca/~watrous/Papers/QuantumInteractiveProofs.pdf

[KW88] M. Karchmer and A. Wigderson. Monotone circuits for connectivity require superlogarithmic depth, Proceedings of ACM STOC'88, pp. 539-550, 1988.

[KW93] M. Karchmer and A. Wigderson. On span programs, Proceedings of IEEE Complexity'93, pp. 102-111, 1993.

[KW98] J. Köbler and O. Watanabe. New collapse consequences of NP having small circuits, SIAM Journal on Computing 28(1):311-324, 1998. http://www.informatik.hu-berlin.de/forschung/gebiete/algorithmenII/Publikationen/Papers/collapse.ps.gz

[KW15] J. Kwisthout. Tree-width and the computational complexity of MAP approximations in Bayesian networks, Journal of Artificial Intelligence Research 53:699-720, 2015. http://www.socsci.ru.nl/johank/tree-width_PP.pdf

##### L

[Lad75] R. Ladner. On the structure of polynomial time reducibility, Journal of the ACM 22:155-171, 1975.

[Lau83] C. Lautemann. BPP and the polynomial time hierarchy, Information Processing Letters 17:215-218, 1983.

[Lee02] T. Lee. Arithmetical definability over finite structures, Mathematical Logic Quarterly, Vol. 49(4), 2003. http://www.lri.fr/~lee/arith.pdf.

[Lev73] L. A. Levin. Universal search problems (in Russian), Problemy Peredachi Informatsii 9(3):265-266, 1973.

[Lev86] L. A. Levin. Average case complete problems, SIAM Journal on Computing, 15:285-286, 1986.

[LFK+90] C. Lund, L. Fortnow, H. Karloff, and N. Nisan. Algebraic methods for interactive proofs, Proceedings of IEEE FOCS'90, pp. 1-10, 1990. http://people.cs.uchicago.edu/~fortnow/papers/ip.ps

[Li93] L. Li. On the Counting Functions, PhD thesis, University of Chicago, 1993.

[LiRe93] M. Liskiewicz, R. Reischuk. The complexity world below logarithmic space, Proceedings of the Structure in Complexity Theory Conference, 1993, 64-78.

[Li11] Y. D. Li. BQP and PPAD, Electronic Colloquium on Computational Complexity TR11-103, 2011.

[LL76] R. Ladner and N. A. Lynch. Relativization of questions about log space computability, Mathematical Systems Theory 10:19-32, 1976.

[LMN93] N. Linial, Y. Mansour, and N. Nisan. Constant depth circuits, Fourier transform, and learnability, Journal of the ACM 40(3):607-620, 1993.

[LMT97] K. Lange, P. McKenzie, and A. Tapp. Reversible space equals deterministic space (extended abstract), Proceedings of IEEE FOCS'97, pp. 45-50, 1997.

[LP82] H. R. Lewis and C. H. Papadimitriou. Symmetric space-bounded computation, Theoretical Computer Science 19:161-187, 1982.

[LS74] E. A. Lamagna and J. E. Savage Combinational complexity of some monotone functions, FOCS 140-44, 1974.

[Lut91] J. H. Lutz. An upward measure separation theorem, Theoretical Computer Science 81:127-135, 1991.

[Lut93] J. H. Lutz. The quantitative structure of exponential time, Proc. 8th Structure in Complexity Theory Conference, (IEEE Comput. Soc. Press, 1993) 158-175. [10]

[LV97] M. Li and P. Vitányi. An Introduction to Kolmogorov Complexity and Its Applications (second edition), Springer, 1997.

##### M

[M08] L. Malka. How to achieve perfect simulation, and a complete problem for non-interactive perfect zero-knowledge. IACR 5th Theory of Cryptography Conference (TCC), 2008. [11].

[Mah82] S. R. Mahaney. Sparse complete sets for NP: Solution of a conjecture by Berman and Hartmanis, Journal of Computer and System Sciences 25:130-143, 1982.

[May94] E. Mayordomo. Almost every set in exponential time is P-bi-immune, Theoretical Computer Science 136(2):487-506, 1994.

[May94b] E. Mayordomo. Contributions to the study of resource-bounded measure, PhD thesis, Universitat Politecnica de Catalunya, 1994.

[MS89] E. W. Mayr and A. Subramanian. The complexity of circuit value and network stability, Proceedings of the Fourth Annual Conference on Structure in Complexity Theory, pp.114-123, 1989.

[MC00] C. Moore and J. P. Crutchfield. Quantum automata and quantum grammars, Theoretical Computer Science 237:275-306, 2000.

[Mel00] D. Melkebeek. The zero-one law holds for BPP, Theoretical Computer Science, Volume 244, Issues 1-2, 6 August 2000, Pages 283-288.

[Mes99] J. Messner. On optimal algorithms and optimal proof systems, Lecture Notes in Computer Science 1563:541-550, 1999.

[Mil76] G. Miller. Riemann's hypothesis and tests for primality, Journal of Computer and System Sciences, 13:300-317, 1976.

[Mil92] P. B. Miltersen. Circuit depth relative to a random oracle, Information Processing Letters 42(6):295-298, 1992.

[MN02] C. Moore and M. Nilsson. Parallel quantum computation and quantum codes, SIAM Journal on Computing 31(3):799-815, 2002. arXiv:quant-ph/9808027.

[Mon80] B. Monien. On a subclass of pseudopolynomial problems, Mathematical Foundations of Computer Science (MFCS'80), Springer LNCS 88, pp. 414-425, 1980.

[Moo99] C. Moore. Quantum circuits: fanout, parity, and counting, ECCC TR99-032.

[Mor01] T. Morioka. Classification of search problems and their definability in bounded arithmetic, master's thesis, University of Toronto, 2001. ECCC TR01-082.

[MP75] D. E. Muller and F. P. Preparata. Bounds to complexities of networks for sorting and for switching, Journal of the ACM 22:195-201, 1975.

[MP91] N. Megiddo and C. H. Papadimitriou. On total functions, existence theorems, and computational complexity, Theoretical Computer Science 81(2):317-324, 1991.

[MR95] R. Motwani and P. Raghavan. Randomized Algorithms, Cambridge University Press, 1995.

[MS02] K. Mulmuley and M. Sohoni. Geometric complexity theory I: An approach to the P vs. NP and related problems, SIAM Journal on Computing 31(2):496-526, 2002.

[Muc56] A. A. Muchnik. On the unsolvability of the problem of reducibility in the theory of algorithms, Doklady Akademii Nauk SSSR 108:194-197, 1956.

[MV99] P. B. Miltersen and N. V. Vinodchandran. Derandomizing Arthur-Merlin games using hitting sets, Proceedings of IEEE FOCS'99, pp. 71-80, 1999.

[MVV87] K. Mulmuley, U. V. Vazirani, and V. V. Vazirani. Matching is as easy as matrix inversion, Proceedings of ACM STOC'87, pp. 345-354, 1987.

[MVW99] P. B. Miltersen, N. V. Vinodchandran, and O. Watanabe. Super-polynomial versus half-exponential circuit size in the exponential hierarchy, Proceedings of the 5th Annual Conference on Computing and Combinatorics (COCOON'99), pp. 210-220, Lecture Notes in Computer Science 1627, Springer-Verlag, 1999.

[MW05] C. Marriott and J. Watrous. Quantum Arthur-Merlin Games, Computational Complexity, 14(2):122-152, 2005. arXiv:cs/0506068.

##### N

[NC00] M. Nielsen and I. Chuang. Quantum Computation and Quantum Information, Cambridge University Press, 2000.

[NHK00] M. Nakanishi, K. Hamaguchi, and T. Kashiwabara. Ordered quantum branching programs are more powerful than ordered probabilistic branching programs under a bounded-width restriction, Proceedings of COCOON'2000 (Computing and Combinatorics), Springer LNCS 1858, pp. 467-476, 2000.

[Nie02] G. Niemann and J. R. Woinowski. The Growing Context-Sensitive Languages Are the Acyclic Context-Sensitive Languages, Developments in Language Theory. LNCS 2295, pp. 197-205. </span>

[Nis02] T. Nishino. Mathematical models of quantum computation, New Gen. Comput. 20 (2002), no 4, 317-337.

[Nis92] N. Nisan. RL is contained in SC, Proceedings of ACM STOC'92, pp. 619-623, 1992.

[NR97] M. Naor and O. Reingold. Number-theoretic constructions of efficient pseudorandom functions, Proceedings of IEEE FOCS'97, pp. 458-467, 1997.

[NR98] R. Niedermeier and P. Rossmanith. Unambiguous computations and locally definable acceptance types, Theoretical Computer Science 194:137-161, 1998.

[NRR01] M. Naor, O. Reingold, and A. Rosen. Pseudo-random functions and factoring, ECCC TR01-064.

[NS05] A. Nickelsen and B. Schelm. Average-case computations - comparing AvgP, HP, and Nearly-P, Proceedings of IEEE Complexity'2005, pp. 235-242, 2005. http://www.thi.uni-hannover.de/forschung/publikationen/daten/ni-sc05.pdf.

[NSW92] N. Nisan, E. Szemerédi, and A. Wigderson. Undirected connectivity in O(log1.5n) space, Proceedings of IEEE FOCS'92, pp. 24-29, 1992.

[NT95] N. Nisan and A. Ta-Shma. Symmetric logspace is closed under complement, Proceedings of ACM STOC'95, pp. 140-146, 1995. ECCC TR94-003.

[NW94] N. Nisan and A. Wigderson. Hardness versus randomness, Journal of Computer and System Sciences 49:149-167, 1994.

[NY03] H. Nishimura and T. Yamakami. Polynomial time quantum computation with advice, arXiv:quant-ph/0305100, ECCC TR03-059, 2003.

[NY03b] H. Nishimura and T. Yamakami. An algorithmic argument for query complexity lower bounds of advised quantum computation, arXiv:quant-ph/0312003, 2003.

##### O

[Ogi94] M. Ogihara. On serializable languages, International Journal of Foundations of Computer Science 5(3-4):303-318, 1994.

[OH93] M. Ogihara and L. Hemachandra. A complexity theory for feasible closure properties, Journal of Computer and System Sciences 46(3):295-325, 1993.

[Oka96] T. Okamoto. On relationships between statistical zero-knowledge proofs, Proceedings of ACM STOC'96, 1996.

[OKS+94] P. Orponen, K.-I. Ko, U. Schöning, and O. Watanabe. Instance complexity, Journal of the ACM 41:96-121, 1994.

[Ost91] R. Ostrovsky. One-way functions, hard on average problems and statistical zero-knowledge proofs, Proceedings of IEEE Complexity'91, pp. 51-59, 1991.

[OW93] R. Ostrovsky and A. Wigderson. One-way functions are essential for non-trivial zero-knowledge, Proceedings of the 2nd Israel Symposium on Theory of Computing and Systems (ISTCS-93), 1993.

##### P

[Pap83] C. H. Papadimitriou. Games against nature, Proceedings of IEEE FOCS'83, pp. 446-450, 1983.

[Pap90] C. H. Papadimitriou. On graph-theoretic lemmata and complexity classes, Proceedings of IEEE FOCS'90, pp. 794-801, 1990.

[Pap94b] C. H. Papadimitriou. On the complexity of the parity argument and other inefficient proofs of existence, Journal of Computer and System Sciences 48(3):498-532, 1994.

[Per07] K. Pervyshev. On heuristic time hierarchies, Proceedings of the 22nd Annual IEEE Conference on Computational Complexity, 347-357, 2007.

[Pos44] E. L. Post. Recursively enumerable sets of positive integers and their decision problems, Bulletin of the American Mathematical Society 50:284-316, 1944.

[PP00] S. Parker and M. B. Plenio. Efficient factorization with a single pure qubit and log N mixed qubits, Physical Review Letters 85:3049, 2000. arXiv:quant-ph/0001066.

[PPS+83] W. J. Paul, N. Pippenger, E. Szemerédi, and W. T. Trotter. On determinism versus nondeterminism and related problems, Proceedings of IEEE FOCS'83, pp. 429-438, 1983.

[PPS14] P. Papakonstantinou, D. Scheder, and H. Song. Overlays and limited memory communication, Proceedings of IEEE CCC'14, pp. 298-308, 2014.

[Pra74] V. R. Pratt. The power of negative thinking in multiplying Boolean matrices, STOC '74: Proceedings of the sixth annual ACM Symposium on Theory of Computing, 80-83, 1974.

[Pra75] V. R. Pratt. Every prime has a succinct certificate, SIAM Journal on Computing, 4:214-220, 1975.

[PS86] R. Paturi and J. Simon. Probabilistic communication complexity, Journal of Computer and System Sciences, 33(1):106-123, 1986.

[PV04] A. Pavan and N. V. Vinodchandran. TR04-053.

[PY84] C. H. Papadimitriou and M. Yannakakis. The complexity of facets (and some facets of complexity), Journal of Computer and System Sciences 28:244-259, 1984.

[PY88] C. H. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes, Proceedings of ACM STOC'88, pp. 229-234, 1988.

[PY96] C. H. Papadimitriou and M. Yannakakis. On limited nondeterminism and the complexity of the VC dimension, Journal of Computer and System Sciences 53(2):161-170, 1996.

[PZ83] C. H. Papadimitriou and S. Zachos. Two remarks on the power of counting, Proceedings of the 6th GI Conference in Theoretical Computer Science, Lecture Notes in Computer Science Vol. 145, Springer-Verlag, pp. 269-276, 1983.

##### R

[RA00] K. Reinhardt and E. Allender. Making nondeterminism unambiguous, SIAM Journal on Computing 29:1118-1131, 2000. ECCC TR97-014, DIMACS TR 97-46.

[Rab60] M. O. Rabin. Degree of difficulty of computing a function and a partial ordering of recursive sets, Tech Report No. 2, Hebrew University, 1960.

[Rac82] C. Rackoff. Relativized questions involving probabilistic algorithms, Journal of the ACM 29(1):261-268, 1982.

[Raz05] R. Raz. Quantum information and the PCP theorem, to appear in Proc. IEEE FOCS, 2005. ECCC TR05-038.

[Raz85] A. A. Razborov. Lower bounds on the monotone complexity of some Boolean functions, Dokl. Akad. Nauk SSSR 281(4):798-801, 1985. English translation in Soviet Math. Dokl. 31:354-357, 1985.

[Raz85b] A. A. Razborov. A lower bound on the monotone network complexity of the logical permanent, Mat. Zametky 37(6):887-900, 1985. English translation in Russian Mathematical Notes 37:485-493, 1985.

[Raz87] A. A. Razborov. Lower bounds for the size of circuits of bounded depth with basis {&,}, Mathematicheskie Zametki 41(4):598-607, 1987. English translation in Math. Notes. USSR 41(4):333-338, 1987.

[Raz92] A. A. Razborov. On the distributional complexity of disjointness, Theoretical Computer Science 106(2):385-390, 1992.

[Raz94] A. A. Razborov. On provably disjoint NP-pairs, ECCC TR94-006, 1994.

[Reg02] K. Regan. Understanding the Mulmuley-Sohoni approach to P vs. NP, Bulletin of the EATCS 78, October 2002. http://people.cs.uchicago.edu/~fortnow/beatcs/column78.pdf.

[Rei04] O. Reingold. Undirected st-connectivity in log-space, ECCC TR04-094, 2004.

[RR95] K. Regan and J. Royer. On Closure Properties of Bounded two-Sided Error Complexity Classes, Math. Systems Theory, 28 (1995) 229-243. ftp://ftp.cis.syr.edu/users/royer/coinflips.ps

[RR97] A. A. Razborov and S. Rudich. Natural proofs, Journal of Computer and System Sciences 55(1):24-35, 1997. ECCC TR94-010.

[RS98] A. Russell and R. Sundaram. Symmetric alternation captures BPP, Computational Complexity 7(2):152-162, 1998.

[RS10] A. Razborov and A. Sherstov. The sign-rank of AC0, SIAM Journal on Computing 39(5):1833-1855, 2010.

[RTV05] O. Reingold and L. Trevisan and S. Vadhan. Pseudorandom walks in biregular graphs and the RL vs. L problem, ECCC TR05-022, 2004.

[Rub88] R. Rubinstein. Structural Complexity Classes of Sparse Sets: Intractability, Data Compression, and Printability, PhD Thesis, Northeastern University (Boston, MA), 1988.

[Rud97] S. Rudich. Super-bits, demi-bits, and NP/qpoly-natural proofs, RANDOM: International Workshop on Randomization and Approximation Techniques in Computer Science, Lecture Notes in Computer Science, Springer-Verlag, 1997.

[Rus85] D. A. Russo. Structural Properties of Complexity Classes. PhD thesis, UC Santa Barbara, 1985.

[RUV12] B. W. Reichardt, F. Unger, and U. Vazirani. A classical leash for a quantum system: Command of quantum systems via rigidity of CHSH games, Nature 496:456–460, 2013.

[Ruz81] W. L. Ruzzo. On uniform circuit complexity, Journal of Computer and System Sciences 22(3):365-383, 1971.

[RV97] K. Regan and H. Vollmer. "Gap-languages and log-time complexity classes", Theoretical Computer Science 188(1–2):101–116, 1997.

[RW01] S. Reith and K. Wagner. On Boolean lowness and Boolean highness, Theoretical Computer Science 261(2):305-321, 2001.

##### S

[San07] R. Santhanam. Circuit lower bounds for Merlin-Arthur classes, Electronic Colloquium on Computational Complexity, Report TR07-005.

[Sav70] W. Savitch. Relationships between nondeterministic and deterministic tape complexities, Journal of Computer and System Sciences 4(2):177-192, 1970.

[Sch02a] M. Schaefer and C. Umans. Completeness in the Polynomial-Time Hierarchy: A Compendium, Sigact News September, 2002.

[Sch02b] M. Schaefer and C. Umans. Completeness in the Polynomial-Time Hierarchy: Part II, Sigact News December, 2002.

[Sch03] P. Schnoebelen. Oracle circuits for branching-time model checking, Proceedings of ICALP 2003, pp. 790-801, 2003.

[Sch78] C. P. Schnorr. Satisfiability Is Quasilinear Complete in NQL, Journal of the ACM 25(1):136-145, 1978.

[Sch83] U. Schöning. A low and a high hierarchy within NP, Journal of Computer and System Sciences 27:14-28, 1983.

[Sch86] U. Schöning. Complete Sets and Closeness to Complexity Classes, Mathematical Systems Theory 19:29-41, 1986. DOI:10.1007/BF01704904

[Sel79] A. Selman. P-selective sets, tally languages, and the behavior of polynomial time reducibilities in NP, Mathematical Systems Theory 13(1):55-65, 1979.

[Sch2015] M. Schwarz. An exponential time upper bound for quantum Merlin Arthur games with unentangled provers, arXiv:1510.08447, 2015.

[SES05] E. Allender, S. Datta, and S. Roy. The directed planar reachability problem, Proceedings of FSTTCS, #1373 in Computer Science

[SF98] H. T. Siegelmann and S. Fishman. Analog computation with dynamical systems, Physica 120D, p. 214, 1998.

[SFM78] J. Seiferas, M. Fischer, and A. Meyer. Separating nondeterministic time complexity classes, Journal of the ACM 25:146-167, 1978.

[Sha90] A. Shamir. IP=PSPACE, Proceedings of IEEE FOCS'90, pp. 11-15, 1990.

[She59] J. C. Shepherdson. The reduction of two-way automata to one-way automata, IBM Journal of Research and Development, 3:198-200, 1959.

[She08] A. A. Sherstov. Separating AC0 from depth-2 majority circuits, Computational Complexity, 17(2):149-178, 2008. http://www.cs.utexas.edu/~sherstov/publications/pdf/cc08hsmat.pdf

[Shi03] Y. Shi. Quantum and classical tradeoffs, arXiv:quant-ph/0312213, ECCC TR04-023, 2003.

[Sho97] P. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Journal on Computing 26(5):1484-1509, 1997. arXiv:quant-ph/9508027.

[Sho99] R. A. Shore. The recursively enumerable degrees, Handbook of Recursion Theory (E. Griffor, ed.), pp. 169-197, North-Holland, Amsterdam, 1999.

[Sip82] M. Sipser. On relativization and the existence of complete sets, Proceedings of ICALP'82, Springer-Verlag Lecture Notes in Computer Science volume 140, pp. 523-531, 1982.

[Sip92] M. Sipser. The history and status of the P versus NP question, Proceedings of ACM STOC'92, pp. 603-618, 1992.

[SM02] L. J. Stockmeyer and A. R. Meyer. Cosmological lower bound on the circuit complexity of a small problem in logic, Journal of the ACM 49(6):753-784, 2002. http://theory.lcs.mit.edu/~meyer/stock-circuit-jacm.pdf.

[SM03] R. Santhanam and D. van Melkebeek. Holographic proofs and derandomization, Proceedings of the 18th Annual IEEE Conference on Computational Complexity, 269-283.

[Smo87] R. Smolensky. Algebraic methods in the theory of lower bounds for Boolean circuit complexity, Proceedings of ACM STOC'87, pp. 77-82, 1987.

[SP98] U. Schöning and R. Pruim. Gems of Theoretical Computer Science, Springer-Verlag, 1998.

[Spa02] R. Špalek. Quantum circuits with unbounded fan-out, arXiv:quant-ph/0208043, 2002.

[SS04] A. Selman and S. Sengupta. Polylogarithmic-round interactive proofs for coNP collapse the exponential hierarchy, Proceedings of IEEE Complexity 2004, pp. 82-90, 2004. ECCC TR04-007.

[SS77] R. Solovay and V. Strassen. A fast Monte-Carlo test for primality, SIAM Journal on Computing, 6:84-86, 1977.

[Sto76] L. J. Stockmeyer. The polynomial hierarchy, Theoretical Computer Science 3:1-22, 1976.

[Sto85] L. J. Stockmeyer. On approximation algorithms for #P, SIAM Journal on Computing 14:849-861, 1985.

[STT05] H. Spakowski, M. Thakur, and R. Tripathi. Quantum and Classical Complexity Classes: Separations, Collapses, and Closure Properties, Inform. and Comput. 200 (2005), no. 1, 1--34. http://web.umr.edu/~thakurk/publications/quantum-j.pdf

[SU05] R. Shaltiel and C. Umans. Pseudorandomness for approximate counting and sampling, Proceedings of IEEE Complexity'2005, pp. 212-226, 2005. http://www.cs.haifa.ac.il/~ronen/online_papers/derand-ccc-final.ps.

[Sub94] A. Subramanian. A New Approach to Stable Matching Problems, SIAM Journal on Computing 23(4), 671-701, 1994.

[Sud78] I. Sudborough. On the tape complexity of deterministic context-free languages, Journal of the ACM 25(3):405-414, 1978.

[SV97] A. Sahai and S. Vadhan. A complete promise problem for statistical zero-knowledge, Proceedings of IEEE FOCS'97. http://www.eecs.harvard.edu/~salil/papers/complete-abs.html.

[SZ95] M. Saks and S. Zhou. RSPACE(s) is contained in DSPACE(s3/2), Proceedings of IEEE FOCS'95, pp. 344-353, 1995.

[Sze87] R. Szelepcsényi. The method of forcing for nondeterministic automata, Bulletin of the EATCS 33:96-100, 1987.

[Szep94] A. Szepietowski. Turing Machines With Sublogarithmic Space, Lecture Notes in Computer Science, volume 843.

##### T

[Tan07] T. Tantau. Logspace Optimization Problems and Their Approximability Properties, Theory of Computing Systems, 41:327-350, 2007.

[Tar88] E. Tardos. The gap between monotone and non-monotone circuit complexity is exponential, Combinatorica, 8:141-142, 1988.

[Tar89] G. Tardos. Query complexity, or why is it difficult to separate NPA intersect coNPA from PA by random oracles A, Combinatorica, 9:385-392, 1989.

[Tha98] J. S. Thathachar. On Separating the Read-k-Times Branching Program Hierarchy, Proceedings of the 30th ACM Symposium on Theory of Computing, pp. 653-662, 1998. ECCC TR98-02, DOI:10.1145/276698.276881.

[Tod89] S. Toda. On the computational power of PP and P, Proceedings of IEEE FOCS'89, pp. 514-519, 1989.

[Tor00] J. Torán. On the hardness of graph isomorphism, Proceedings of IEEE FOCS'2000, pp. 180-186, 2000.

[Tor88] J. Torán. Structural Properties of the Counting Hierarchies, Ph.D Theis, 1988.

[Tor90] J. Torán. Counting the number of solutions, Proceedings of 15th Conference on Mathematical Foundations of Computer Science (MFCS), pp. 121-135, Springer-Verlag Lecture Notes in Computer Science 452, 1990.

[Tor91] J. Torán. Complexity classes defined by counting quantifiers, Journal of the ACM 38:753-774, 1991.

[Tur36] A. M. Turing. On computable numbers, with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society 2(42):230-265, 1936; 2(43):544-546, 1937.

[TV02] L. Trevisan and S. Vadhan. Pseudorandomness and average-case complexity via uniform reductions, Proceedings of CCC'2002, pp. 129-138, 2002.

##### U

[Uma98] C. Umans. The minimum equivalent DNF problem and shortest implicants, Proceedings of IEEE FOCS'98, pp. 556-563, 1998.

##### V

[Vad06] S. Vadhan. An Unconditional Study of Computational Zero Knowledge, ECCC TR06-056.

[Val03] L. G. Valiant. Three problems in computer science, Journal of the ACM 50(1):96-99, 2003.

[Val76] L. G. Valiant. Relative complexity of checking and evaluating, Information Processing Letters, 5:20-23, 1976.

[Val79] L. G. Valiant. The complexity of computing the permanent, Theoretical Computer Science, 8:189-201, 1979.

[Val79b] L. G. Valiant. Completeness classes in algebra, Proceedings of ACM STOC'79, pp. 249-261, 1979.

[Var82] M. Vardi. Complexity of relational query languages, Proceedings of ACM STOC'82, pp. 137-146, 1982.

[Ven91] H. Venkateswaran. Properties that characterize LOGCFL, Journal of Computer and System Sciences 43(2):380-404, 1991.

[Ver92] N. K. Vereshchagin. On the power of PP, Proceedings of IEEE Complexity'92, pp. 138-143, 1992.

[Ver95] N. K. Vereshchagin. Oracle separation of complexity classes and lower bounds for perceptrons solving separation problems, Izvestiya Mathematics 59(6):1103-1122, 1995.

[Vid03] G. Vidal. Efficient classical simulation of slightly entangled quantum computations, Physical Review Letters 91:147902, 2003. arXiv:quant-ph/0301063.

[Vin04] N. V. Vinodchandran. Counting complexity of solvable group problems, SIAM Journal on Computing 33(4):852-869, 2004, http://www.cse.unl.edu/~vinod/papers/SIAMFinal.ps.

[Vin04b] N. V. Vinodchandran. A note on the circuit complexity of PP, ECCC TR04-056, 2004.

[VSB+83] L. G. Valiant, S. Skyum, S. Berkowitz, and C. Rackoff. Fast parallel computation of polynomials using few processors, SIAM Journal on Computing 12(4):641-644, 1983.

[VV85] U. V. Vazirani and V. V. Vazirani. Random polynomial time equals semi-random polynomial time, Proceedings of IEEE FOCS'85, pp. 417-428, 1985.

[VV86] L. G. Valiant and V. V. Vazirani. NP is as easy as detecting unique solutions, Theoretical Computer Science 47(3):85-93, 1986.

[Vya03] M. Vyalyi. QMA=PP implies that PP contains PH, ECCC TR03-021, 2003.

##### W

[Wag86] K. W. Wagner. The complexity of combinatorial problems with succinct input representation, Acta Informatica 23:325-356, 1986.

[Wag88] K. W. Wagner. Bounded query computation, Proceedings of IEEE Complexity'88, pp. 260-277, 1988.

[WW85] G. Wechsung. On the Boolean closure of NP, Proceedings of the International Conference on Fundamentals of Computation Theory, LNCS volume 199, Springer-Verlag, pp. 485-493.

[Wat00] J. Watrous. Succinct quantum proofs for properties of finite groups, Proceedings of IEEE FOCS'2000, pp. 537-546, 2000. arXiv:cs.CC/0009002.

[Wat02] J. Watrous. Limits on the power of quantum statistical zero-knowledge, to appear in Proceedings of IEEE FOCS'2002. arXiv:quant-ph/0202111.

[Wat09] J. Watrous. Quantum Computational Complexity, Encyclopedia of Complexity and Systems Science, Springer, pp. 7174-7201, 2009. arXiv:quant-ph/0804.3401.

[Wat87] O. Watanabe. Comparison of polynomial time completeness notions, Theoretical Computer Science 53:249-265, 1987.

[Wat99] J. Watrous. PSPACE has constant-round quantum interactive proof systems, Proceedings of IEEE FOCS'99, pp. 112-119, 1999. arXiv:cs.CC/9901015.

[Wat99b] J. Watrous. Space-bounded quantum complexity, Journal of Computer and System Sciences 59(2):281-326, 1999. http://www.cpsc.ucalgary.ca/%7Ejwatrous/papers/jcss_space.ps.

[Wat15] T. Watson. The complexity of deciding statistical properties of samplable distributions, Theory of Computing, 11:1-34, 2015.

[Weg87] I. Wegener. The Complexity of Boolean Functions, New York: Wiley 1987.

[Weg88] I. Wegener. On the Complexity of Branching Programs and Decision Trees for Clique Functions, Journal of the ACM 35(2):461-471, 1988. DOI:10.1145/42282.46161.

[Weh06] S. Wehner. Entanglement in interactive proof systems with binary answers, In Proceedings of the 23rd Annual Symposium on Theoretical Aspects of Computer Science, volume 3884 of Lecture Notes in Computer Science, pages 162–171. Springer, 2006

[Wig06] A. Wigderson P, NP, and mathematics--a computational complexity perspective, 2006 mimeo. [www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/W06/W06.pdf].

[Wil85] C. Wilson. Relativized circuit complexity, Journal of Computer and System Sciences 31:169-181, 1985.

[Wil11] R. Williams. Non-uniform ACC circuit lower bounds, To appear in IEEE Conference on Computational Complexity 2011.

[Wol94] M. J. Wolf. Nondeterministic circuits, space complexity and quasigroups, Theoretical Computer Science 125:295–313, 1994.

##### Y

[Yap83] C. Yap. Some consequences of non-uniform conditions on uniform classes, Theoretical Computer Science, (1983), 26, 287-300.

[Yam99] T. Yamakami. Polynomial time samplable distributions, J. Complexity 15 (1999), no. 4, 557-574. ECCC TR95-039.

[Yan81] M. Yannakakis. Algorithms for acyclic database schemas, Proceedings of VLDB (Very Large Databases), 1981.

[Yan91] M. Yannakakis. Expressing combinatorial optimization problems by linear programs, Journal of Computer and System Sciences, 43(3):441-466, 1991.

[Yao85] A. C.-C. Yao. Separating the polynomial hierarchy by oracles, Proceedings of IEEE FOCS'85, pp. 1-10, 1985.

[Yao89] A. C.-C. Yao. Circuits and local computation, Proceedings of ACM STOC'89, pp. 186-196, 1989.

[Yao90] A. C.-C. Yao. On ACC and threshold circuits, Proceedings of IEEE FOCS'90, pp. 619-627, 1990.

[Yao90b] A. C.-C. Yao. Coherent functions and program checkers, Proceedings of ACM STOC'90, 1990.

[Yao93] A. C.-C. Yao. Quantum circuit complexity, Proceedings of IEEE FOCS'93, pp. 352-361, 1993.

[Yes83] Y. Yesha. On certain polynomial-time truth-table reducibilities of complete sets to sparse sets, SIAM Journal on Computing, 12(3):411-425, 1983. DOI:10.1137/0212027

##### Z

[Zac88] S. Zachos. Probabilistic quantifiers and games, Journal of Computer and System Sciences 36(3):433-451, 1988.

[ZH86] S. Zachos and H. Heller. A decisive characterization of BPP. Information and Control, 69(1–3):125–135, 1986.

[Zuc91] D. Zuckerman. Simulating BPP using a general weak random source, Algorithmica 16 (1996), no. 4-5, 367--391 http://www.cs.utexas.edu/users/diz/pubs/bpp.ps.