CPS 240: Computational Complexity

Department of Computer Science

John H. Reif
Spring Semester, 2009

Required Class Text Books: (digital text books [AB] and [G] used by permission)

[Pap] Christos Papadimitriou. Computational Complexity. Addison-Wesley Longman, 1994. Errata.
[AB] Sanjeev Arora and Boaz Barak, Computational Complexity: A Modern Approach, digital preprint of yet to be published book, Princeton University.
[G] Oded Goldreich, Computational Complexity: A Conceptual Perspective, digital preprint of yet to be published book, Weizmann Institute.

Additional Readings in Complexity Theory: ([T] used by permission)

[GJ] M. Garey and D. Johnson. Computers and intractability: A guide to NP-Completeness. W. H. Freeman & Co., 1979.
[HMU] J. Hopcroft, R. Motwani, and J. Ullman. Introduction to automata theory, language, and computation. Addison Wesley, 2001

[T] Martin Tompa, Introduction to Computational Complexity, unpublished digital notes, University of Washington

S. C. Kleene, Origins of recursive function theory, Annals of the History of Computing, 3 (1981), 52-67.
M. Davis, Why Godel didn't have Church's thesis, Information and Control 54 (1982), 3-24.
J. Hartmanis, Observations about the development of theoretical computer science, Annals of the History of Computing, 3 (1981), 42-51.
M. Sipser, The history and status of the P versus NP question, Proc. 24th Annual ACM Symposium. Theory of Computing, 1992, 603-619.

J.E. Hopcroft, Turing machines, Scientific American, 250:5 (1984), 86-98.
A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proc. London Math. Scoiety, 2 (1936), 230-265.

J. Hartmanis and R. E. Stearns, On the computational complexity of algorithms, Transactions of AMS, 117 (1965), 285-306.
M. Rabin, Degree of difficulty of computing a function and a partial ordering of recursive sets, Tech Rept 2, Hebrew University, 1960.

R. E. Ladner, On the structure of polynomial time reducibility, J. ACM 22 (1975), 155-171.
R. E. Ladner, N. A. Lynch, and A. L. Selman, A comparison of polynomial time reducibilities, Theoretical Computer Science 1 (1975), 103-123.

J. Canny, Some algebraic and geometric computations in PSPACE, Proc. 20th Annual ACM Sympos. Theory of Comput., 1988, 460-467.
M. Fischer and M. Rabin, Super-exponential complexity of Persburger arithmetic, in Complexity of Computation, (R. M. Kapr, ed.), SIAM.

[CKS] A. Chandra, D. Kozen, and L. Stockmeyer, Alternation, JACM 28 (1981), 114-133.

[BF] L. Babai and L. Fortnow, Arithmetization: A new method in structural complexity theory Comput. Complexity 1 (1991), 41-66.
[L] C. Lund, The Power of Interaction, MIT Press, 1992.

[ALMSS] S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy, Proof verification and intractability of approximation problems, J. ACM 45 (1998), 501-555.
[AS] S. Arora and S. Safra, Probabilistic checking of proofs: A new characterization of NP, J. ACM 45 (1998), 70-122.
[H1] J. Hastad, Clique is hard to approximate within n^{1-e}, Acta Math 182 (1999), 105-142.
[H2] J. Hastad, Some optimal inapproximability results, J. ACM 48 (2001), 798-859.
[HPS] S. Hougardy, H.J. Promel, and A. Steger, Probabilistically checkable proofs and their consequences for approximation algorithms, Discrete Math. 136 (1994), 175-223.

[A] Scott Aaronson, Is P Versus NP Formally Independent? Bulletin of the EATCS 81: 109-136 (2003).