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 ...

Many phrase alignment models operate over the combinatorial space of bijective phrase alignments. We prove that finding an optimal alignment in this space is NP-hard, while computing alignment expectations is #P-hard. On the other hand, we show that the problem of finding an optimal alignment can be cast as an integer linear program, which provides a simple, declarative approach to Viterbi infe...

Implications of a formal context obey Armstrong rules, which allows one to define a minimal (in the number of implications) implication basis, called Duquenne–Guigues basis or stem base in the literature. In this paper we show how implications are reduced to functional dependencies and prove that the problem of determining the size of the stem base is a #P-complete problem. © 2007 Published by ...

where Sn is the symmetric group of permutations on {1, 2, . . . , n}. Unlike the determinant, computing the exact value of the permanent of a given matrix is known to be #P-hard. Thus, most research has focused on finding approximation algorithms for and proving upper and lower bounds for restricted classes of matrices. A sharp upper-bound on the permanent the case of 0− 1 matrices was proved b...

Many hard problems can be solved efficiently for problem instances that can be decomposed by tree decompositions of small width. In particular for problems beyond NP, such as #P-complete counting problems, tree decomposition-based methods are particularly attractive. However, finding an optimal tree decomposition is itself an NP-hard problem. Existing methods for finding tree decompositions of ...