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An algebraic characterisation of complexity for valued constraints
 In: Proceedings CP’06. Volume 4204 of Lecture Notes in Computer Science., SpringerVerlag
, 2006
"... Classical constraint satisfaction is concerned with the feasibility of satisfying a collection of constraints. The extension of this framework to include optimisation is now also being investigated and a theory of socalled soft constraints is being developed. In this extended framework, tuples of ..."
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Cited by 26 (8 self)
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is a sum of cost functions chosen from some fixed set of available cost functions, known as a valued constraint language. We show in this paper that when the costs are rational numbers or infinite the complexity of a soft constraint problem is determined by certain algebraic properties of the valued
Algebraic characterisation of oneway patterns
"... We give a complete structural characterisation of the map the positive branch of a oneway pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition [4], which is then further analysed to obtain the primary structure of the matrix M, represe ..."
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We give a complete structural characterisation of the map the positive branch of a oneway pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition [4], which is then further analysed to obtain the primary structure of the matrix M
1Algebraic Characterisation of the H ∞ and H2 Norms for Linear ContinuousTime Periodic Systems∗
"... It is wellknown that linear, periodically timevarying, continuoustime systems are formally equivalent to socalled lifted representations that are shiftinvariant, but have spatially infinitedimensional inputs and outputs. By shift invariance, corresponding frequencydomain representations can ..."
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the impulsive response of the system, can also be defined. The purpose of this paper is to establish finitedimensional, algebraic characterisations of these norms, for linear continuoustime periodic systems. 1
CuntzKrieger algebras of directed graphs
, 1996
"... We associate to each rowfinite directed graph E a universal CuntzKrieger C  algebra C (E), and study how the distribution of loops in E affects the structure of C (E). We prove that C (E) is AF if and only if E has no loops. We describe an exit condition (L) on loops in E which allow ..."
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Cited by 213 (45 self)
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We associate to each rowfinite directed graph E a universal CuntzKrieger C  algebra C (E), and study how the distribution of loops in E affects the structure of C (E). We prove that C (E) is AF if and only if E has no loops. We describe an exit condition (L) on loops in E which
Some characterisations of supported algebras
 J. Pure Appl. Algebra
"... Abstract. We give several equivalent characterisations of left (and hence, by duality, also of right) supported algebras. These characterisations are in terms of properties of the left and the right parts of the module category, or in terms of the classes L0 and R0 which consist respectively of the ..."
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Cited by 2 (1 self)
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Abstract. We give several equivalent characterisations of left (and hence, by duality, also of right) supported algebras. These characterisations are in terms of properties of the left and the right parts of the module category, or in terms of the classes L0 and R0 which consist respectively
CHARACTERISATIONS OF NELSON ALGEBRAS
"... Abstract. Nelson algebras arise naturally in algebraic logic as the algebraic models of Nelson’s constructive logic with strong negation. This note gives two characterisations of the variety of Nelson algebras up to term equivalence, together with a characterisation of the finite Nelson algebras up ..."
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Cited by 1 (0 self)
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Abstract. Nelson algebras arise naturally in algebraic logic as the algebraic models of Nelson’s constructive logic with strong negation. This note gives two characterisations of the variety of Nelson algebras up to term equivalence, together with a characterisation of the finite Nelson algebras up
A characterisation of firstorder constraint satisfaction problems
 LOGICAL METHODS COMPUT. SCI
, 2007
"... We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction problem is firstorder definable: we show the general problem to ..."
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Cited by 35 (11 self)
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We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction problem is firstorder definable: we show the general problem
Closure Properties of Constraints
 Journal of the ACM
, 1997
"... Many combinatorial search problems can be expressed as `constraint satisfaction problems', and this class of problems is known to be NPcomplete in general. In this paper we investigate the subclasses which arise from restricting the possible constraint types. We first show that any set of cons ..."
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Cited by 180 (23 self)
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that all known classes of tractable constraints over finite domains can be characterised by such an algebraic closure property. Finally, we describe a simple computational procedure which can be used to determine the closure properties of a given set of constraints. This procedure involves solving a
Results 1  10
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563