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...

A P systems based general framework for modeling ecosystems dynamics will be described. Roughly speaking, the idea is to use several regions (environments) that can be connected, each of them containing a probabilistic P system with active membranes (having identical skeleton for every environment). Some real case studies will be displayed, discussing the usefulness of this tool in simulating c...

Plate-based probabilistic models combine a few relational constructs with Bayesian networks, so as to allow one to specify large and repetitive probabilistic networks in a compact and intuitive manner. In this paper we investigate the combined, data and domain complexity of plate models, showing that they range from polynomial to #P-complete to #EXP-complete.

We study the problem of computing the reliability of a network operated using the OSPF protocol where links fail with given independent probabilities. Our measure of reliability is the expected lost demand in the network. Computing this measure is #P-complete, so we developed approximation methods based on related work for circuit-switched networks. Preliminary results show the robustness of op...

Many studies have reported strong associations between substance misuse and violent crime. But the population impact of people diagnosed with substance use disorders on such crime is not known. Calculating the population impact and the relative importance of different classes of drugs is necessary to estimate the likely public health effect of any developments in services and treatment interven...