Abstract
The P =?NP problem has provided much of the primary motivation for developments in structural complexity theory. Recent results show that even after twenty years, contributions to the P=?NP problem, as well as other problems, still inspire new efforts. The purpose of this talk is to explain some of these results to theoreticians who do not work in structural complexity theory.
The preparation of this paper was supported in part by the National Science Foundation under Grant CCR-8913584 and by the Alexander von Humboldt Stiftung while the author visited the FacilitÄt für Informatik, UniversitÄt-Ulm, Germany.
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T. Baker, J. Gill, and R. Solovay. Relativizations of the P=? NP problem, SIAM J. Computing 4 (1975), 431–442.
J. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity I, Springer-Verlag, 1988.
J. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity II, Springer-Verlag, 1990.
C. Bennett and J. Gill. Relative to a random oracle, P A≠NP A ≠ co-NP A with probability 1, SIAM J. Computing 10 (1981), 96–113.
L. Berman and J. Hartmanis. On isomorphism and density of NP and other complete sets, SIAM J. Computing 6 (1977), 305–322.
R. Book. Some Observations on separating complexity classes, SIAM J. Computing 20 (1991), 246–258.
R. Book, T. Long, and A. Selman. Quantitative relativizations of complexity classes, SIAM J. Computing 13 (1984), 461–487.
R. Book, J. Lutz, and K. Wagner. On complexity classes and algorithmically random languages, STACS 92, Lecture Notes in Computer Sci., 577, Springer-Verlag (1992), 319–328.
J.-Y. Cai. With proability one, a random oracle separates PSPACE from the polynomial-time hierarchy, J. Comput. Systems Sci. 38 (1989), 68–85.
A. Cobham. The intrinsic computational difficulty of functions, Prod. 1964 International Congress for Logic, Methodology and Philosophy of Science, North Holland (1964), 24–30.
S. Cook. The complexity of theorem-proving procedures, Proc. 3rd ACM Symp. Theory of Computing (1971), 151–158.
M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman & Co., 1979.
R. Karp. Reducibility among combinatorial problems, in R. Miller and J. Thatcher (eds.), Complexity of Computer Computation, Plenum Press (1972), 85–104.
R. Karp and R. Lipton. Turing machines that take advice, L'Enseignement Mathématique 28 2nd series (1982), 191–209.
S. Kurtz. On the random oracle hypothesis, Info. and Control 57 (1983), 40–47.
L. Levin. Universal sequential search problems, Probl. Pered. Inform. IX (1973), 115–116. English translation in Probl. Information Transmission 9 (1973), 265–266.
M. Li and P. Vitanyi. Kolmogorov complexity and its applications, in J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, vol. A, Elsevier Sci. Publishers (1990), 187–254.
S. Mahaney. Sparse complete sets for NP: solution of a conjecture by Berman and Hartmanis, J. Comput. and Systems Sci. 25 (1982), 130–143.
P. Martin-Löf. On the definition of random sequences, Info. and Control 9 (1966), 602–619.
P. Martin-Löf. Complexity oscillations in infinite binary sequences, Zeitschrift für Wahrscheinlichkeitstheory und Verwandte Gebiete 19 (1971), 225–230.
M. Ogiwara and A. Lozano. On one query self-reducible sets, Proc. 6th IEEE Conference on Structure in Complexity Theory (1991), 139–151.
M. Ogiwara and O. Watanabe. On polynomial bounded truth-table reducibility of NP sets to sparse sets, SIAM J. Computing 20 (1991), 471–483.
H. Rogers. Theory of Recursive Functions and Effective Computability, McGraw-Hill, 1967.
B. Trakhtenbrot. A survey of Russian approaches to Perebor (brute-force search) algorithms, Annals History of Computing 6 (1984), 384–399.
O. Watanabe, A comparison of polynomial-time completeness notions, Theoret. Comput. Sci. 54 (1987), 249–265.
A. Yao. Separating the polynomial-time hierarchy by oracles, Proc. 26th IEEE Symp. Foundations of Comput. Sci. (1985), 1–10.
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Book, R.V. (1992). Relativizations of the P=? NP and other problems: Some developments in structural complexity theory. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_70
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