## Polynomial-Time Membership Comparable Sets (1994)

Citations: | 31 - 4 self |

### BibTeX

@MISC{Ogihara94polynomial-timemembership,

author = {Mitsunori Ogihara},

title = {Polynomial-Time Membership Comparable Sets},

year = {1994}

}

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### OpenURL

### Abstract

This paper studies a notion called polynomial-time membership comparable sets. For a function g, a set A is polynomial-time g-membership comparable if there is a polynomialtime computable function f such that for any x 1 ; \Delta \Delta \Delta ; xm with m g(maxfjx 1 j; \Delta \Delta \Delta ; jx m jg), outputs b 2 f0; 1g m such that (A(x 1 ); \Delta \Delta \Delta ; A(xm )) 6= b. The following is a list of major results proven in the paper. 1. Polynomial-time membership comparable sets construct a proper hierarchy according to the bound on the number of arguments. 2. Polynomial-time membership comparable sets have polynomial-size circuits. 3. For any function f and for any constant c ? 0, if a set is p f(n)-tt -reducible to a Pselective set, then the set is polynomial-time (1 + c) log f(n)-membership comparable. 4. For any C chosen from fPSPACE;UP;FewP;NP;C=P;PP;MOD 2 P; MOD 3 P; \Delta \Delta \Deltag, if C ` P-mc(c log n) for some c ! 1, then C = P. As a corollary of the last tw...