We prove that the problem of counting the number of colourings of the vertices of a graph with at most two colours, such that the colour classes induce connected subgraphs is #P-complete. We also show that the closely related problem of counting the number of cocircuits of a graph is #P-complete.

Answering a problem posed by Nakhleh, we prove that counting the number of phylogenetic trees inferred by a (binary) phylogenetic network is #P-complete. An immediate consequence of this result is that counting the number of phylogenetic trees commonly inferred by two (binary) phylogenetic networks is also #P-complete.

We solve the problem of computing the residual reliability (the RES problem) for all classes of P-threshold graphs for which efficient structural characterizations based on decomposition to indecomposable components have been established. In particular, we give a constructive proof of existence of linear algorithms for computing residual reliability of pseudodomishold, domishold, matrogenic and...

We consider the complexity of combining bodies of evidence according to the rules of the Dempster{Shafer theory of evidence. We prove that, given as input a set of tables representing basic probability assignments m1; : : : ; mn over a frame of discernment , and a set A , the problem of computing the combined basic probability value (m1: : :mn)(A) is #P-complete. As a corollary, we obtain that ...

In this paper we prove that calculating the average covering tree value recently proposed as a single-valued solution of graph games is #P-complete.

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...

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, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta...

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...