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Classifying the Complexity of Constraints Using Finite Algebras
TLDR
It is shown that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra is explored. Expand
The complexity of soft constraint satisfaction
TLDR
It is shown that many tractable sets of soft constraints, both established and novel, can be characterised by the presence of particular multimorphisms and the notion of multimorphism is used to give a complete classification of complexity for the Boolean case which extends several earlier classification results for particular special cases. Expand
Constraint Satisfaction Problems and Finite Algebras
TLDR
It is shown that any restricted set of constraint types can be associated with a finite universal algebra and the result is a dichotomy theorem which significantly generalises Schaefer's dichotomy for the Generalised Satisfiability problem. Expand
Quantified Constraints: Algorithms and Complexity
TLDR
This paper considers a more general framework for constraint satisfaction problems which allows arbitrary quantifiers over constrained variables, rather than just existential quantifiers, and shows that the complexity of such extended problems is determined by the surjective polymorphisms of the constraint predicates. Expand
Algebraic approach to promise constraint satisfaction
TLDR
A new class of problems that can be viewed as algebraic versions of the (Gap) Label Cover problem are introduced, and it is shown that every PCSP with a fixed constraint language is equivalent to a problem of this form. Expand
Polymorphisms, and How to Use Them
This article describes the algebraic approach to Constraint Satisfaction Problem that led to many developments in both CSP and universal algebra. No prior knowledge of universal algebra is assumed.
Reasoning about temporal relations: The tractable subalgebras of Allen's interval algebra
TLDR
This article provides the final step in the classification of complexity for satisfiability problems over constraints expressed in Allen's interval algebra, and shows that this algebra contains exactly eighteen maximal tractable subalgebras, and reasoning in any fragment not entirely contained in one of these subalagbras is NP-complete. Expand
Skew Bisubmodularity and Valued CSPs
TLDR
It is proved that submodularity with respect to a total order and skew bisubmodularity give rise to the only tractable cases, and, in all other cases, again, Max Cut can be expressed. Expand
Skew Bisubmodularity and Valued CSPs
TLDR
This work investigates the case when the variables can take three values and identifies a new infinite family of conditions that includes bisubmodularity as a special case and which can collectively be called skew bisubModularity. Expand
The complexity of maximal constraint languages
TLDR
This paper systematically study the complexity of all maximal constraint languages, that is, languages whose expressive power is just weaker than that of the language of all constraints. Expand
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