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...

For any q > 1, let MODq be a quantum gate that determines if the number of 1’s in the input is divisible by q. We show that for any q, t > 1, MODq is equivalent to MODt (up to constant depth). Based on the case q = 2, Moore [8] has shown that quantum analogs of AC(0), ACC[q], and ACC, denoted QAC (0) wf , QACC[2], QACC respectively, define the same class of operators, leaving q > 2 as an open q...

We prove a complexity dichotomy theorem for the most general form of Boolean #CSP where every constraint function takes values in the complex number field C. This generalizes a theorem by Dyer, Goldberg and Jerrum [11] where each constraint function takes non-negative values. We first give a non-trivial tractable class of Boolean #CSP which was inspired by holographic reductions. The tractabili...

We present an approach to non-uniform complexity in which singlepass instruction sequences play a key part, and answer various questions that arise from this approach. We introduce several kinds of non-uniform complexity classes. One kind includes a counterpart of the well-known non-uniform complexity class P/poly and another kind includes a counterpart of the well-known non-uniform complexity ...