P-Selective Self-Reducible Sets

We show that any p-selective and self-reducible set is in P. As the converse is also true, we obtain a new characterization of the class P. A generalization and several consequences of this theorem are discussed. Among other consequences, we show that under reasonable assumptions auto-reducibility and self-reducibility differ on NP, and that there are non-p-T-mitotic sets in NP.

[1]  Neil Immerman,et al.  Languages that Capture Complexity Classes , 1987, SIAM J. Comput..

[2]  A. Shamir.  IP=PSPACE (interactive proof=polynomial space) , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[3]  Klaus Ambos-Spies.  P-mitotic sets , 1983, Logic and Machines.

[4]  Alan L. Selman,et al.  Reductions on NP and P-Selective Sets , 1982, Theor. Comput. Sci..

[5]  J. Edmonds.  Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.

[6]  Nicholas Pippenger,et al.  On simultaneous resource bounds , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[7]  Lane A. Hemaspaandra,et al.  Near-Testable Sets , 1991, SIAM J. Comput..

[8]  Joan Feigenbaum,et al.  Languages that are easier than their proofs , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[9]  Neil Immerman,et al.  Expressibility as a complexity measure: results and directions , 1987, SCT.

[10]  José L. Balcázar,et al.  Structural complexity 1 , 1988 .

[11]  Ronald V. Book,et al.  Tally Languages and Complexity Classes , 1974, Inf. Control..

[12]  Alan L. Selman,et al.  Promise Problems Complete for Complexity Classes , 1988, Inf. Comput..

[13]  Neil Immerman,et al.  Sparse Sets in NP-P: EXPTIME versus NEXPTIME , 1985, Inf. Control..

[14]  Peter van Emde Boas,et al.  Twenty Questions to a P-Selector , 1993, Inf. Process. Lett..

[15]  Paul Young,et al.  Using Self-Reducibilities to Characterize Polynomial Time , 1993, Inf. Comput..

[16]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[17]  Richard E. Ladner,et al.  Mitotic recursively enumerable sets , 1973, Journal of Symbolic Logic.

[18]  Ker-I Ko.  On Self-Reducibility and Weak P-Selectivity , 1983, J. Comput. Syst. Sci..

[19]  R.E. Ladner,et al.  A Comparison of Polynomial Time Reducibilities , 1975, Theor. Comput. Sci..

[20]  C. Jockusch.  Semirecursive sets and positive reducibility , 1968 .

[21]  Mitsunori Ogihara,et al.  P-selective sets, and reducing search to decision vs. self-reducibility , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.