Complexity Zoo References

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[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.

[Aar10] S. Aaronson. BQP and the Polynomial Hierarchy, Proceedings of ACM STOC 2010. arXiv:0910.4698, ECCC TR09-104.

[Aar18] S. Aaronson. PDQP/qpoly = ALL, arXiv:1805.08577.

[ABOE08] D. Aharonov, M. Ben-Or, E. Eban. Interactive Proofs for Quantum Computations, arXiv:0810.5375.

[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

[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, B. Fefferman and P. Shor. The power of unentanglement Theory of Computing, 5(1):1-42, 2009 arXiv:0804.0802

[ABF+94] J. Aspnes, R. Beigel, M. L. Furst, and S. Rudich. The expressive power of voting polynomials, Combinatorica 14(2):135-148, 1994.

[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.),

[ACJ+21] M. Arenas, L. A. Croquevielle, R. Jayaram, and C. Riveros. #NFA admits an FPRAS: Efficient Enumeration, Counting, and Uniform Generation for Logspace Classes. Journal of the ACM 68(6):48:1-48:40, 2021.

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

[Adl78] L. Adleman. Two theorems on random polynomial time. FOCS 78.

[AD14] S. Aaronson and A. Drucker. A Full Characterization of Quantum Advice, SIAM Journal on Computing 43(3):1131–1183, 2014. arXiv:1004.0377.

[AFM01] L. Antuñes, L. Fortnow, and D. van Melkebeek. Computational depth, Proceedings of IEEE Complexity'01, pp. 266-273, 2001.

[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, S. Irani, and J. Kempe;stad. The power of quantum systems on a line. Comm. Math. Physics, vol. 287, no. 1, pp. 41-65 (2009) arXiv:0705.4077

[Agr01] M. Agrawal. For completeness, sublogarithmic space is no space, Information Processing Letters (82), 2001-2002, iss. 6, 321-325.

[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, SIAM Journal of Computing, 36(4):845-888, 2006,

[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, Information and Computation, 204(5):835-852, 2006 ECCC TR02-037

[AK06] S. Aaronson and G. Kuperberg. Quantum Versus Classical Proofs and Advice. Theory of Computing 3(7):129-157, 2007 arXiv:quant-ph/0604056

[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.

[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.

[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.

[Amb14] A. Ambainis. On physical problems that are slightly more difficult than QMA, Proceedings of the 2014 IEEE 29th Conference on Computational Complexity, 2014. arXiv:quant-ph/1312.4758.

[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

[Ani+23] Joshua Ani et al. Complexity of Motion Planning of Arbitrarily Many Robots: Gadgets, Petri Nets, and Counter Machines. 2023. arxiv: [1]

[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, Journal of the ACM 45(5) 753-782, 1998.

[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.

[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.

[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.

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

[AW09] S. Aaronson and J. Watrous. Closed Timelike Curves Make Quantum and Classical Computing Equivalent, Proceedings of the Royal Society A 465:631-647, 2009. arXiv:0808.2669.

[AW90] E. Allender and K. W. Wagner. Counting hierarchies: polynomial time and constant depth circuits, Bulletin of the EATCS 40, February 1990.


[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.

[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.

[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. DOI

[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.

[BBR94] D. A. M. Barrington, R. Beigel, and S. Rudich. Representing Boolean functions as polynomials modulo composite integers, Computational Complexity, 4:367-382, 1994.

[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.

[BCH86] P. Beame, S. Cook, and J. Hoover. Log depth circuits for division and related problems, SIAM Journal on Computing 15:994-1003, 1986

[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.

[BCK+14] H. Buhrman, R. Cleve, M. Koucky, B. Loff, and F. Speelman. Computing with a full memory: catalytic space, Symposium on the Theory of Computing (STOC) 857-866, 2014.

[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.

[BCHTV17] A. Bouland, L. Chen, D. Holden, J. Thaler, and P. N. Vasudevan. On the Power of Statistical Zero Knowledge, Foundations of Computer Science, pp. 708-719, 2017. arXiv:[2].

[BCY11] F.G.S.L. Brandão, M. Christandl, and J. Yard. A quasipolynomial-time algorithm for the quantum separability problem. Proceedings of ACM STOC'11, pp. 343-352, 2011. arXiv:1011.2751.

[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.

[Bei89] R. Beigel. On the relativized power of additional accepting paths, Proceedings of IEEE Complexity'89, pp. 216-224, 1989.

[Bei94] R. Beigel. Perceptrons, PP, and the polynomial hierarchy, Computational Complexity 4:339-349, 1994.

[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

[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.

[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.

[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.

[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.

[BG69] R. Book and S. Greibach. Quasi-realtime languages, Proceedings of ACM STOC pp. 15-18, 1969.

[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.

[BG98] R. Beigel and J. Goldsmith. Downward separation fails catastrophically for limited nondeterminism classes, SIAM Journal on Computing 17(5):1420-1429, 1998.

[BG94] M. Bellare and S. Goldwasser. The complexity of decision versus search, SIAM Journal on Computing 23(1):91-119, 1994.

[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.

[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] [3]

[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.

[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.

[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, Proceedings of IEEE Complexity'2000, 2000.

[BKS95] R. Beigel, M. Kummer, and F. Stephan. Approximable sets, Information and Computation 120(2):304-314, 1995.

[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.

[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.

[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, 2000. Also Proc. 5th Kurt Gödel Colloq. KGS 1997, Springer LNCS 1289, pp. 114-127. MLQ KGS 1997

[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.

[BT04] H. Buhrman and L. Torenvliet. Separating complexity classes using structural properties, Proceedings of IEEE Complexity 2004, pp. 130-138, 2004.

[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.

[Buss17] S. Buss. Uniform Proofs of ACC Representations, Archive for Mathematical Logic 56(5–6):639–669, 2017.

[BV97] E. Bernstein and U. Vazirani. Quantum complexity theory, SIAM Journal on Computing, 26(5):1411-1473, 1997.

[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. Vereshchagin, 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.


[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.

[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.

[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.

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