Essentials of Constraint Programming

Principles and Practice of Constraint Programming - CP 2005

2005

Self Cite

Abstract. We motivate and develop a linear logic declarative semantics for CHR ∨ , an extension of the CHR programming language that integrates concurrent committed choice with backtrack search and a predefined underlying constraint handler. We show that our semantics maps each of these aspects of the language to a distinct aspect of linear logic. We show how we can use this semantics to reason about derivations in CHR ∨ and we present strong theorems concerning its soundness and completeness.

Section: Constraint Handling Rules With Disjunctionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Linear-Logic Semantics for Constraint Handling Rules

Betz

Principles and Practice of Constraint Programming - CP 2005

2005

Self Cite

“…CHR [Frü98,FA03,Frü08] manipulates conjunctions of constraints (relations, predicates, atoms) that reside in a constraint store. In the following, the metavariables H, G, B and C denote conjunctions of constraints, denoting head (parts of the head), guard, body of a rule and constraints from a state, respectively.…”

Section: Constraint Handling Rules (Chr)mentioning

confidence: 99%

Quasi-Linear-Time Algorithms by Generalisation of Union-Find in CHR

Lecture Notes in Computer Science

2008

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Abstract. The union-find algorithm can be seen as solving simple equations between variables or constants. With a few lines of code change, we generalise its implementation in CHR from equality to arbitrary binary relations. By choosing the appropriate relations, we can derive fast incremental algorithms for solving certain propositional logic (SAT) problems and polynomial equations in two variables. In general, we prove that when the relations are bijective functions, our generalisation yields a correct algorithm. We also show that bijectivity is a necessary condition for correctness if the relations include the identity function.The rules of our generic algorithm have additional properties that make them suitable for incorporation into constraint solvers: from classical union-find, they inherit a compact solved form and quasi-linear time and space complexity. By nature of CHR, they are anytime and online algorithms. They solve and simplify the constraints in the problem, and can test them for entailment, even when the constraints arrive incrementally.

“…In this section we give an overview of syntax and semantics for Constraint Handling Rules (CHR) [7,8].…”

Section: Constraint Handling Rules (Chr)mentioning

confidence: 99%

Parallelizing Union-Find in Constraint Handling Rules Using Confluence Analysis

2005

Logic Programming

Self Cite

Abstract. Constraint Handling Rules is a logical concurrent committedchoice rule-based language. Recently it was shown that the classical union-find algorithm can be implemented in CHR with optimal time complexity. Here we investigate if a parallel implementation of this algorithm is also possible in CHR. The problem is hard for several reasons: -Up to now, no parallel computation model for CHR was defined. -Tarjan's optimal union-find is known to be hard to parallelize. -The parallel code should be as close as possible to the sequential one. It turns out that confluence analysis of the sequential implementation gives almost all the information needed to parallelize the union-find algorithm under a rather general parallel computation model for CHR.