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...

The paper shows a logspace-reduction from the boolean circuit value problem which demonstrates that any relation subsuming bisimilarity and being subsumed by trace preorder (i.e., language inclusion) is ptime-hard, even for finite acyclic labelled transition systems. This reproves and substantially extends the result of Balcázar, Gabarró and Sántha (1992) for bisimilarity.

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 show a dichotomy theorem for polynomial evaluation. That is, we show that for a given set S, either there exists a VNP-complete family of polynomials associated to S, or the associated fa...

In general, constructing a locally-optimal structure is a little harder than constructing an arbitrary structure, but significantly easier than constructing a globally-optimal structure. A similar situation arises in listing. In counting, most problems are #P-complete, but in approximate counting we observe an interesting reversal of the pattern. Assuming that #BIS is not equivalent to #SAT und...

This paper is motivated by a conjecture [All12, ADF13] that BPP can be characterized in terms of polynomial-time nonadaptive reductions to the set of Kolmogorov-random strings. In this paper we show that an approach laid out in [ADF13] to settle this conjecture cannot succeed without significant alteration, but that it does bear fruit if we consider time-bounded Kolmogorov complexity instead. W...