This chapter surveys counting Constraint Satisfaction Problems (counting CSPs, or #CSPs) and their computational complexity. It aims to provide an introduction to the main concepts and techniques, and present a representative selection of results and open problems. It does not cover holants, which are the subject of a separate chapter. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorith...

We survey recent results on the broad family of problems that can be cast as valued constraint satisfaction problems (VCSPs). We discuss general methods for analysing the complexity of such problems, give examples of tractable cases, and identify general features of the complexity landscape. 1998 ACM Subject Classification F.1.3 Complexity Measures and Classes, G.1.6 Optimization

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This paper presents the basis of Property Grammars, a fully constraintbased theory. In this approach, all kinds of linguistic information is represented by means of constraints. The constraint system constitutes then the core of the theory: it is the grammar, but it also constitutes, after evaluation for a given input, its description. Property Grammars is then a non-generative theory in the se...

We point out that statistical mechanics put a stronger constraint than asymptotic freedom on the number of flavors-in confining gauge theories.

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We study the experimental consequences of a recent theoretical result by Achlioptas et al. that shows that conventional models of random problems are trivially insoluble in the limit. We survey the literature to identify experimental studies that lie within the scope of this result. We then estimate theoretically and measure experimentally the size at which problems start to become trivially in...

Weighted nite-state constraints that can count unboundedly many violations make Optimality Theory more powerful than nite-state transduction (Frank and Satta, 1998). This result is empirically and computationally awkward. We propose replacing these unbounded constraints, as well as nonnite-state Generalized Alignment constraints, with a new class of nite-state directional constraints. We give l...

this study set out to investigate the distribution of the syntactic properties associatedwith the prodrop parameter by persian-speaking l2 learners of english in an attemptto examine the (un)attainability of native-like knowledge and (in)accessibility of ugin adult sla. to do so, 92 participants were assigned into different levels of l2knowledge based on their performances on the oxford placeme...