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...