We consider the #P-complete problem of counting the number of linear extensions of a poset (#LE); a fundamental problem in order theory with applications in a variety of distinct areas. In particular, we study the complexity of #LE parameterized by the well-known decompositional parameter treewidth for two natural graphical representations of the input poset, i.e., the cover and the incomparabi...

It is shown that, with respect to a random oracle, EXP \ P=poly and EXP ? P=poly do not have resource-bounded measure zero in EXP:

This paper addresses the problems of counting proof trees (as introduced by Venkateswaran and Tompa) and counting proof circuits, a related but seemingly more natural question. These problems lead to a common generalization of straight-line programs which we call polynomial replacement systems. We contribute a classification of these systems and we investigate their complexity. Diverse problems...

In this paper we present the model of decision P systems with external output and prove the following main result: if there exists an NP–complete problem that cannot be solved in polynomial time, with regard to the input length, by the deterministic variant of such P systems, constructed in polynomial time, then P 6= NP . From Zandron-FerretiMauri’s theorem it follows that if P 6= NP then no NP...

In this paper, we use resource-bounded dimension theory to investigate polynomial size circuits. We show that for every i ≥ 0, P/poly has ith order scaled p 3 -strong dimension 0. We also show that P/poly i.o. has p 3 -dimension 1/2, p 3 -strong dimension 1. Our results improve previous measure results of Lutz (1992) and dimension results of Hitchcock and Vinodchandran (2004).

03/15/2012 Lecture 16: CS 880: Complexity of Counting Problems Instructor: Jin-Yi Cai Scribe: Chen Zeng For a symmetric, bipartite matrix A ∈ C, we want to prove the following theorem: Theorem 1. If EVAL(A) is not #P-hard, then there exists an m × m purified bipartite matrix A such that EVAL(A) ≡ EVAL(A). Recall the definition of the purified bipartite matrix : Definition 1. Let A ∈ C be a symm...