The complexity of computing the Tutte polynomial T(~/c,x,y) is determined for transversal matroid ,4s and algebraic numbers x and y. It is shown that for fixed x and y the problem of computing T(~,x,y) for JA a transversal matroid is ~pP-complete unless the numbers x and y satisfy (x 1)(y 1) = 1, in which case it is polynomial-time computable. In particular, the problem of counting bases in a t...

Consider a probabilistic graph G in which the edges are perfectly reliable, but vertices may fail with some known probabilities. The 2-terminal reliability of G is defined as the probability that one operational path exists between a given source and destination pair vertices of G. This 2-terminal reliability problem is known to be #P-complete for general graphs but solvable in polynomial time ...

Aslam presents an algorithm he claims will count the number of perfect matchings in any incomplete bipartite graph with an algorithm in the function-computing version of NC, which is itself a subset of FP. Counting perfect matchings is known to be #P-complete; therefore if Aslam's algorithm is correct, then NP=P. However, we show that Aslam's algorithm does not correctly count the number of per...

BACKGROUND Brazil has severe socioeconomic inequalities, resulting in major oral health problems for the Brazilian elderly, such as tooth loss and, consequently, a need for oral rehabilitation. The aim of this study was to evaluate inequalities in complete denture need among older Brazilian adults in relation to social determinants at individual and contextual levels. METHODS This retrospecti...

Given a symmetric matrix M ∈ {0, 1, ∗}D×D, anM -partition of a graph G is a function from V (G) to D such that no edge of G is mapped to a 0 of M and no non-edge to a 1. We give a computer-assisted proof that, when |D| = 4, the problem of counting the M -partitions of an input graph is either in FP or is #P-complete. Tractability is proved by reduction to the related problem of counting list M ...

We prove that the problem of counting the number of stable states in a given Hopfield net is #P-complete and the problem of computing the size of the attraction domain of a given stable state is NP-hard.

In social choice settings with linear preferences, random dictatorship is known to be the only social decision scheme satisfying strategyproofness and ex post efficiency. When also allowing indifferences, random serial dictatorship (RSD) is a well-known generalization of random dictatorship that retains both properties. RSD has been particularly successful in the special domain of random assign...

The aim of the present clinical report was to describe the use of a patient's extensive fixed prosthesis, where the supporting teeth were hopeless, for fabricating an interim immediate complete denture. The present procedure was used to replicate the vertical dimension, phonetic and aesthetic of the existing fixed prostheses as part of an immediate denture and a final complete denture.

The permanent of matrices has wide applications in many fields of science and engineering. It is, however, a #P-complete problem in counting. The best-known algorithm for computing the permanent, which is due to Ryser [Combinatorial Mathematics, The Carus Mathematical Monographs, vol. 14, Mathematical Association of America, Washington, DC, 1963], runs O(n2 ) in time. It is possible to speed up...

In this paper, we consider the problem of counting output patterns of a circuit with gates having fan-in 2. For the case where every gate computes the same Boolean function f , Uchizawa, Wang, Morizumi and Zhou (2013) proved that the problem is solvable in polynomial time if f is the parity function or any degenerate function, while this problem is #P-complete if f is one of the other functions...