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 ...

In this paper ZnO nanorods and nanodots (with and without a SiO2 buffer layer) were grown on p-Si, forming p–n heterojunctions. The nanorod devices showed no visible electroluminescence (EL) emission but showed rectifying behavior. Covering around 60% of the length of the nanorods with PMMA produced an ideality factor of 3:91 0:11 together with a reverse saturation current of 6:53 4:2 10 8 A. U...

We consider the computational complexity of the Market equilibrium problem by exploring the structural properties of the Leontief exchange economy. We prove that, for economies guaranteed to have a market equilibrium, finding one with maximum social welfare or maximum individual welfare is NP-hard. In addition, we prove that counting the number of equilibrium prices is #P-hard.

We review Andr\'e Luiz Barbosa's paper"P != NP Proof,"in which the classes P and NP are generalized and claimed to be proven separate. We highlight inherent ambiguities in Barbosa's definitions, and show that attempts to resolve this ambiguity lead to flaws in the proof of his main result.