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Bibliography Bibliography [AB06] Sanjeev Arora and Boaz Barak. Computational complexity: A modern approach. Initial draft kindly placed by the authors on the web, 2006. [AGP94] W. R. Alford, A. Granville, and C. Pomerance. There are infinitely many Carmichael numbers. Annals of Mathematics, 139:703–722, 1994. [Bab90] L´aszl´o Babai. E-mail and the unexpected power of interaction. In Structure in Complexity Theory Conference, pages 30–44, 1990. [Ben62] James Bennett. On Spectra. PhD thesis, Princeton University, 1962. [Ber84] Stuart J. Berkowitz. On computing the determinant in small parallel time using a small number of processors. Information Processing Letters, 18(3):147–150, 1984. [BM77] John Bell and Mosh´e Machover. A course in mathematical logic. North-Holland, 1977. [BP96] Paul Beame and Toniann Pitassi. Simplified and improved reso- lution lower bounds. In FOCS, pages 274–282, 1996. [CLRS01] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. McGraw-Hill Book Company, 2001. Second Edition. [CN06] Stephen A. Cook and Phuong Nguyen. Foundations of proof complexity: Bounded arithmetic and propositional translations. Manuscript available from www.cs.toronto.edu/~sacook/, 2006. 149 150 BIBLIOGRAPHY [Coo71] Stephen A. Cook. The complexity of theorem proving proce- dures. In Conference record of Third Annual ACM Symposium on Theory of Computing, pages 151–158, May 1971. [Coo76] Stephen A. Cook. A short proof of the pigeon hole principle using extended resolution. SIGACT News, 1976. [Coo85] Stephen A. Cook. A taxonomy of problems with fast parallel algorithms. Information and Computation, 64(13):2–22, 1985. [Coo00] Stephen A. Cook. The P versus NP problem. Manuscript pre- pared for the Clay Mathematics Institute for the Millennium Prize Problems, 2000. [Coo06] Stephen A. Cook. Csc 438f/240f lecture notes. Available at the author’s web site, http://www.cs.toronto.edu/~sacook/, 2006. [Dev05] Keith Devlin. The Millennium Problems. Granta Books, 2005. [GJ79] Michael R. Garey and David S. Johnson. Computers and In- tractability. Bell Telephone Laboratories, 1979. [HO02] Lane A. Hemaspaandra and Mitsunori Ogihara. The Complexity Theory Companion. Springer, 2002. [Hof98] P. Hoffman. The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth. Hyperion, 1998. [Imm99] Neil Immerman. Descriptive Complexity. Springer-Verlag, 1999. [KL80] Richard M. Karp and Richard J. Lipton. Some connections be- tween nonuniform and uniform complexity classes. In STOC, pages 302–309, 1980. [Koz06] Dexter Kozen. Theory of Computation. Springer, 2006. [KR87] Richard M. Karp and Michael O. Rabin. Efficient randomized pattern-matching algorithms. IBM Journal of Research and De- velopment, 31(2):249–260, 1987. [Liv05] Mario Livio. The equation that couldn’t be solved. Simon & Schus- ter, 2005. Michael Soltys - Draft version - September 13, 2007 BIBLIOGRAPHY 151 [MA04] Nitin Saxena Manindra Agrawal, Neeraj Kayal. Primes is in P. Annals of Mathematics, 160(2):781–793, 2004. [MR95] Rajeev Motwani and Prabhakar Raghavan. Randomized Algo- rithms. Cambridge University Press, 1995. [MV97] M. Mahajan and V. Vinay. Determinant: Combinatorics, algo- rithms, and complexity. Chicago Journal of Theoretical Computer Science, 1997(5):1–26, December 1997. [Pap94] Christos H. Papadimitriou. Computational Complexity. Addison- Wesley, 1994. [RA00] Klaus Reinhardt and Eric Allender. Making nondeterminism un- ambiguous. SIAM J. Comput., 29(4):1118–1131, 2000. [She59] J.C. Shepherdson. The reduction of two-way automata to one- way automata. IBM Journal of Research and Development, 3:198–200, 1959. [Sip06a] Michael Sipser. Introduction to the theory of computation. Thom- son, 2006. Second Edition. [Sip06b] Michael Sipser. Introduction to the Theory of Computation. Thompson, 2006. 2nd Edition. [SP95] Uwe Scho¨ning and Randall Pruim. Gems of Theoretical Computer Science. Springer, 1995. [Str83] Howard Straubing. A combinatorial proof of the Cayley-Hamilton Theorem. Discrete Mathematics, 43:273–279, 1983. [Tur36] A. M. Turing. On computable numbers, with an application to the entscheidungsproblem. Proceedings of the London Mathemat- ical Society, 42:230–265, 1936. [Val92] L.G. Valiant. Why is boolean complexity theory difficult? In M. Paterson, editor, Boolean Function Complexity, volume 169 of London Mathematical Society Lecture Notes Series, pages 84– 94. Cambridge University Press, New York, 1992. Michael Soltys - Draft version - September 13, 2007.
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