Polynomial-time 1-Turing reductions from #PH to #P

Polynomial-time kernel reductions

Today, the computational complexity of equivalence problems such as the graph isomorphism problem and the Boolean formula equivalence problem remain only partially understood. One of the most important tools for determining the (relative) difficulty of a computational problem is the many-one reduction, which provides a way to encode an instance of one problem into an instance of another. In equ...

Polynomial-Time Reductions, NP-Completeness, and Approximations 1

Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization

The universality of polynomial time Turing equivalence

We show that polynomial time Turing equivalence and a large class of other equivalence relations from computational complexity theory are universal countable Borel equivalence relations. We then discuss ultrafilters on the invariant Borel sets of these equivalence relations which are related to Martin’s ultrafilter on the Turing degrees.

A Small Span Theorem for P/Poly-Turing Reductions

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 red...