Beautiful structures: an appreciation of the contributions of Alan Selman

M. Agrawal and V. Arvind. Quasi-linear truth--table reductions to P-selective sets. Theoretical Computer Science, 158(1--2):361--370, 1996.

L. Adleman and K. Manders. Reducibility, randomness, and intractibility. In Proceedings of the 9th ACM Symposium on Theory of Computing, pages 151--153. ACM Press, May 1977.

J. Balcázar, R. Book, T. Long, U. Schöning, and A. Selman. Sparse oracles and uniform complexity classes. In Proceedings of the 25th IEEE Symposium on Foundations of Computer Science, pages 308--313. IEEE Computer Society Press, October 1984.

J. Balcázar, R. Book, and U. Schöning. The polynomial-time hierarchy and sparse oracles. Journal of the ACM, 33(3):603--617, 1986.

L. Berman. Polynomial Reducibilities and Complete Sets. PhD thesis, Cornell University, Ithaca, NY, 1977.

L. Babai and L. Fortnow. Arithmetization: a new method in structural complexity theory. Computational Complexity, 1(1):41--66, 1991.

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

L. Berman and J. Hartmanis. On isomorphisms and density of NP and other complete sets. SIAM Journal on Computing, 6(2):305--322, 1977.

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

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

R. Book, T. Long, and A. Selman. Qualitative relativizations of complexity classes. Journal of Computer and System Sciences, 30(3):395--413, 1985.

R. Book. Bounded query machines: On NP and PSPACE. Theoretical Computer Science, 15:27--39, 1981.

R. Book. Towards a theory of relativizations: Positive relativizations. In Proceedings of the 4th Annual Symposium on Theoretical Aspects of Computer Science, pages 1--21. Springer-Verlag Lecture Notes in Computer Science #247, 1987.

R. Book. Restricted relativizations of complexity classes. In J. Hartmanis, editor, Computational Complexity Theory, pages 47--74. American Mathematical Society, 1989. Proceedings of Symposia in Applied Mathematics #38.

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

T. Baker and A. Selman. A second step toward the polynomial hierarchy. Theoretical Computer Science, 8:177--187, 1979.

R. Chang, B. Chor, O. Goldreich, J. Hartmanis, J. Hástad, and D. Ranjan. The Random Oracle Hypothesis is false. Journal of Computer and System Sciences, 49(1):24--39, 1994.

J. Cai, V. Chakaravarthy, L. Hemaspaandra, and M. Ogihara. Competing provers yield improved Karp-Lipton collapse results. Information and Computation, 198(1):1--23, 2005.

Clay Mathematics Institute. www.claymath.org/millennium-problems. URL verified June 2014.

D. Du and K. Ko. Theory of Computational Complexity. John Wiley and Sons, 2000.

S. Even, A. Selman, and Y. Yacobi. The complexity of promise problems with applications to public-key cryptography. Information and Control, 61(2):159--173, 1984.

S. Fenner, L. Fortnow, and S. Kurtz. The Isomorphism Conjecture holds relative to an oracle. SIAM Journal on Computing, 25(1):193--206, 1996.

S. Fenner, S. Homer, M. Ogiwara, and A. Selman. Oracles that compute values. SIAM Journal on Computing, 26(4):1043--1065, 1997.

P. Faliszewski and M. Ogihara. Separating the notions of self- and autoreducibility. In Proceedings of the 30th International Symposium on Mathematical Foundations of Computer Science, pages 308--315. Springer Verlag Lecture Notes in Computer Science #3618, August/September 2005.

L. Fortnow and M. Sipser. Are there interactive protocols for co-NP? Information Processing Letters, 28:249--251, 1988.

J. Goldsmith, L. Hemachandra, D. Joseph, and P. Young. Near-testable sets. SIAM Journal on Computing, 20(3):506--523, 1991.

C. Glaser, A. Hughes, A. Selman, and N. Wisiol. Disjoint NP-pairs and propositional proof systems. SIGACT News, 45(4), 2014. In Preparation.

C. Glaser, D. Nguyen, C. Reitwiesner, A. Selman, and M. Witek. Autoreducibility of complete sets for log--space and polynomial-time reductions. In Proceedings of the 40th International Colloquium on Automata, Languages, and Programming, Part I, pages 473--484, July 2013.

C. Glaser, M. Ogihara, A. Pavan, A. Selman, and L. Zhang. Autoreducibility and mitocity. SIGACT News, 40(3):61--76, 2009.

J. Grollmann and A. Selman. Complexity measures for public-key cryptosystems. SIAM Journal on Computing, 17(2):309--335, 1988.

J. Hástad. Computational Limitations of Small-Depth Circuits. MIT Press, 1987.

J. Hartmanis, R. Chang, S. Chari, D. Ranjan, and P. Rohatgi. Relativization: A revisionistic retrospective. Bulletin of the EATCS, 47:144--153, 1992.

L. Hemachandra and A. Hoene. On sets with efficient implicit membership tests. SIAM Journal on Computing, 20(6):1148--1156, 1991.

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

E. Hemaspaandra, A. Naik, M. Ogihara, and A. Selman. P-selective sets and reducing search to decision vs. self-reducibility. Journal of Computer and System Sciences, 53(2):194--209, 1996.

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.

L. Hemaspaandra and M. Ogihara. The Complexity Theory Companion. Springer- Verlag, 2002.

L. Hemaspaandra, M. Ogihara, and G. Wechsung. Reducing the number of solutions of NP functions. Journal of Computer and System Sciences, 64(2):311--328, 2002.

A. Hughes, A. Pavan, N. Russell, and A. Selman. A thirty year old conjecture about promise problems. In Proceedings of the 39th International Colloquium on Automata, Languages, and Programming, Part I, pages 473--484. Springer-Verlag Lecture Notes in Computer Science #7391, July 2012.

L. Hemachandra and R. Rubinstein. Separating complexity classes with tally oracles. Theoretical Computer Science, 92(2):309--318, 1992.

L. Hemaspaandra and J. Rothe. Creating strong, total, commutative, associative oneway functions from any one-way function in complexity theory. Journal of Computer and System Sciences, 58(3):648--659, 1999.

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

L. Hemaspaandra and A. Selman, editors. Complexity Theory Retrospective II. Springer-Verlag, 1997.

S. Homer and A. Selman. Computability and Complexity Theory. Springer-Verlag, 2nd edition, 2011.

L. Hemaspaandra and L. Torenvliet. Theory of Semi-Feasible Algorithms. Springer-- Verlag, 2003.

C. Jockusch. Semirecursive sets and positive reducibility. Transactions of the AMS, 131(2):420--436, 1968.

R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proceedings of the 12th ACM Symposium on Theory of Computing, pages 302--309. ACM Press, April 1980. An extended version has also appeared as: Turing machines that take advice, L'Enseignement Mathématique, 2nd series, 28:191--209, 1982.

K. Ko. On self-reducibility and weak P-selectivity. Journal of Computer and System Sciences, 26(2):209--221, 1983.

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

R. Ladner, N. Lynch, and A. Selman. A comparison of polynomial time reducibilities. Theoretical Computer Science, 1(2):103--124, 1975.

T. Long. Strong nondeterministic polynomial--time reducibilities. Theoretical Computer Science, 21(1):1--25, 1982.

T. Long and A. Selman. Relativizing complexity classes with sparse oracles. Journal of the ACM, 33(3):618--627, 1986.

A. Meyer and M. Paterson. With what frequency are apparently intractable problems difficult? Technical Report MIT/LCS/TM-126, Laboratory for Computer Science, MIT, Cambridge, MA, 1979.

A. Meyer and L. Stockmeyer. The equivalence problem for regular expressions with squaring requires exponential space. In Proceedings of the 13th IEEE Symposium on Switching and Automata Theory, pages 125--129. IEEE Press, October 1972.

A. Naik, J. Rogers, J. Royer, and A. Selman. A hierarchy based on output multiplicity. Theoretical Computer Science, 207(1):131--157, 1998.

D. Nguyen and A. Selman. Non--autoreducible sets for NEXP. In Proceedings of the 31st Annual Symposium on Theoretical Aspects of Computer Science, pages 590--601, March 2014.

M. Ogihara. Polynomial--time membership comparable sets. SIAM Journal on Computing, 24(5):1068--1081, 1995.

M. Ogiwara and O. Watanabe. On polynomial-time bounded truth--table reducibility of NP sets to sparse sets. SIAM Journal on Computing, 20(3):471--483, June 1991.

C. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.

J. Rogers. The Isomorphism Conjecture holds and one-way functions exist relative to an oracle. Journal of Computer and System Sciences, 54(3):412--423, 1997.

M. Rabi and A. Sherman. An observation on associative one-way functions in complexity theory. Information Processing Letters, 64(5):239--244, 1997.

U. Schöning. A low and a high hierarchy within NP. Journal of Computer and System Sciences, 27(1):14--28, 1983.

U. Schöning. Complete sets and closeness to complexity classes. Mathematical Systems Theory, 19(1):29--42, 1986.

A. Selman. On the structure of NP. Notices of the AMS, 21(5):A-498, 1974. Erratum in the same journal, 21(6):310.

A. Selman. Polynomial time enumeration reducibility. SIAM Journal on Computing, 7(4):440--457, 1978.

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

A. Selman. Some observations on NP real numbers and P-selective sets. Journal of Computer and System Sciences, 23(3):326--332, 1981.

A. Selman. Analogues of semirecursive sets and effective reducibilities to the study of NP complexity. Information and Control, 52(1):36--51, 1982.

A. Selman. Reductions on NP and P-selective sets. Theoretical Computer Science, 19(3):287--304, 1982.

A. Selman. Natural self--reducible sets. SIAM Journal on Computing, 17(5):989--996, 1988.

A. Selman, editor. Complexity Theory Retrospective. Springer-Verlag, 1990.

A. Selman. A survey of one-way functions in complexity theory. Mathematical Systems Theory, 25(3):203--221, 1992.

A. Selman. A taxonomy of complexity classes of functions. Journal of Computer and System Sciences, 48(2):357--381, 1994.

A. Selman. Much ado about functions. In Proceedings of the 11th Annual IEEE Conference on Computational Complexity, pages 198--212. IEEE Computer Society Press, May 1996.

A. Shamir. IP = PSPACE. Journal of the ACM, 39(4):869--877, 1992.

L. Stockmeyer. The polynomial--time hierarchy. Theoretical Computer Science, 3(1):1--22, 1976.

A. Selman, Xu M.--R., and R. Book. Positive relativizations of complexity classes. SIAM Journal on Computing, 12(3):565--579, 1983.

L. Valiant. The relative complexity of checking and evaluating. Information Processing Letters, 5(1):20--23, 1976.

O. Watanabe. On hardness of one--way functions. Information Processing Letters, 27(3):151--157, 1988.

A. Yao. Separating the polynomial--time hierarchy by oracles. In Proceedings of the 26th IEEE Symposium on Foundations of Computer Science, pages 1--10. IEEE Computer Society Press, October 1985.