A Small Span Theorem for P/Poly-Turing Reductions
نویسنده
چکیده
This paper investigates the structure of ESPACE under nonuniformTuring reductions that are computed by polynomial size circuits P Poly Turing reductions A Small Span Theorem is proven for such reductions This result says that every language A in ESPACE satis es at least one of the following two conditions i The lower P Poly Turing span of A consisting of all languages that are P Poly Turing reducible to A has measure in ESPACE ii The upper P Poly Turing span of A consisting of all languages to which A is P Poly Turing reducible has pspace measure hence measure in ESPACE The Small Span Theorem implies that every P Poly Turing degree has measure in ESPACE and that there exist languages that are weakly P many one complete but not P Poly Turing complete for ESPACE The method of proof is a signi cant departure from earlier proofs of Small Span Theorems for weaker types of reductions This work was supported in part by National Science Foundation Grant CCR with matching funds from Rockwell International Microware Systems Corporation and Amoco Foundation
منابع مشابه
Completeness and Weak Completeness Under Polynomial-Size Circuits
This paper investigates the distribution and nonuniform complexity of problems that are com plete or weakly complete for ESPACE under nonuniform reductions that are computed by polynomial size circuits P Poly Turing reductions and P Poly many one reductions A tight exponential lower bound on the space bounded Kolmogorov complexities of weakly P Poly Turing complete problems is established A Sma...
متن کاملHard Sets are Hard to Find
We investigate the frequency of complete sets for various complexity classes within EXP under several polynomial-time reductions in the sense of resource bounded measure. We show that these sets are scarce: The sets that are complete under 6 p n ?tt-reductions for NP, the levels of the polynomial-time hierarchy, and PSPACE have p 2-measure zero for any constant < 1. The 6 p n c ?T-complete sets...
متن کاملA Small Span Theorem within P
The development of Small Span Theorems for various complexity classes and re ducibilities plays a basic role in resource bounded measure theoretic investigations of e cient reductions A Small Span Theorem for a complexity class C and reducibil ity r is the assertion that for all sets A in C at least one of the cones below or above A is a negligible small class with respect to C where the cones ...
متن کاملPoly-APX- and PTAS-Completeness in Standard and Differential Approximation
We first prove the existence of natural Poly-APX-complete problems, for both standard and differential approximation paradigms, under already defined and studied suitable approximation preserving reductions. Next, we devise new approximation preserving reductions, called FT and DFT, respectively, and prove that, under these reductions, natural problems are PTAS-complete, always for both standar...
متن کاملToward a Dichotomy Theorem for Polynomial Evaluation
A dichotomy theorem for counting problems due to Creignou and Hermann states that or any finite set S of logical relations, the counting problem #SAT(S) is either in FP, or #P-complete. In the present paper we study polynomial evaluation from this dichotomic point of view. We show that the “hard” cases in the Creignou-Hermann theorem give rise to VNP-complete families of polynomials, and we giv...
متن کامل