On P-immunity of nondeterministic complete sets

We show that every m-complete set for NEXP as well as its complement have an infinite subset in P. This answers an open question first raised by L. Berman (1976).

[1]  Ding-Zhu Du,et al.  A note on one-way functions and polynomial-time isomorphisms , 1986, STOC '86.

[2]  Steven Homer,et al.  Complete Problems and Strong Polynomial Reducibilities , 1992, SIAM J. Comput..

[3]  Juris Hartmanis,et al.  On isomorphisms and density of NP and other complete sets , 1976, STOC '76.

[4]  Leonard Berman,et al.  On the structure of complete sets: Almost everywhere complexity and infinitely often speedup , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[5]  Michael J. Fischer,et al.  Separating Nondeterministic Time Complexity Classes , 1978, JACM.

[6]  Stuart A. Kurtz,et al.  Every polynomial-time 1-degree collapses iff P=PSPACE , 1989, 30th Annual Symposium on Foundations of Computer Science.

[7]  Ding-Zhu Du,et al.  On One-Way Functions and Polynomial-Time Isomorphisms , 1986, Theor. Comput. Sci..

[8]  Edith Hemaspaandra,et al.  Bounded Reductions , 1991, Complexity Theory: Current Research.

[9]  Stanislav Zák,et al.  A Turing Machine Time Hierarchy , 1983, Theor. Comput. Sci..

[10]  Steven Homer.  Structural properties of nondeterministic complete sets , 1990, Proceedings Fifth Annual Structure in Complexity Theory Conference.

[11]  Stanislav Zák.  A Turing machine space hierarchy , 1979, Kybernetika.

[12]  Juris Hartmanis,et al.  On Isomorphisms and Density of NP and Other Complete Sets , 1977, SIAM J. Comput..