Parallelizing Union-Find in Constraint Handling Rules Using Confluence Analysis

Frühwirth, Thom

doi:10.1007/11562931_11

Cited by 20 publications

(37 citation statements)

References 15 publications

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“…We think that we can minimize the use of the debated negation-as-absence [18] by introducing reference counters for the two main constraints. This should also give us the possibility to get a parallel implementation that is derived from the existing one with little modification, similar to what has been done for parallelizing the union-find algorithm in CHR [13].…”

Section: Resultsmentioning

confidence: 99%

“…In each level, quantified basic formulas are locally solved by the rules (1)... (11) and propagated to the embedded sub-formulas by rule (12). Finiteness is checked by rule (9), inconsistent sub-formulas are removed by rule (14) and basic formulas are restored by rule (13). (ii) a bottom-up elimination of quantifiers and reduction of the depth of working formulas done by the rules (15) and (16).…”

Section: •Xmentioning

confidence: 99%

“…In our algorithm, we can distinguish two main parts that are iterated until a solved normal form is reached: (i) In the first part, given a formula (local store), the equations of its parent are copied into it by rule (12), then the local store is simplified by rules (1) to (5), finiteness is checked by rules (6) to (11), and finally rule (13) replaces certain local equations by their counterpart equations from the parent.…”

Section: Chr Rulesmentioning

confidence: 99%

“…The computation is triggered by the presence of the top-most formula together with a direct sub-formula. When rules (1) to (13) have been applied to it, the sub-formula will also be at phase 4 and can now in turn trigger the simplification of the equations in its direct sub-formulas. This means that in part 1, computation proceeds top-down in the tree repre- Note that rules (1) to (5) are a direct implementation of an equation solver for flat rational trees [12,15].…”

Section: Chr Rulesmentioning

confidence: 99%

See 3 more Smart Citations

Toward a first-order extension of Prolog's unification using CHR

Djelloul

Dao²,

Fruehwirth

2007

Proceedings of the 2007 ACM Symposium on Applied Computing

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Prolog, which stands for PROgramming in LOGic, is the most widely used language in the logic programming paradigm. One of its main concepts is unification. It represents the mechanism of binding the contents of variables and can be seen as solving conjunctions of equations over finite or infinite trees. We present in this paper an idea of a first-order extension of Prolog's unification by giving a general algorithm for solving any first-order constraint in the theory T of finite or infinite trees, extended by a relation which allows to distinguish between finite and infinite trees. The algorithm is given in the form of 16 rewriting rules which transform any first-order formula ϕ into an equivalent disjunction φ of simple formulas in which the solutions of the free variables are expressed in a clear and explicit way. We end this paper describing a CHR implementation of our algorithm. CHR (Constraint Handling Rules) has originally been developed for writing constraint solvers, but the constraints here go much beyond implicitly quantified conjunctions of atomic constraints and are considered as arbitrary first-order formulas built on the signature of T . We discuss how we implement nested local constraint stores and what programming patterns and language features we found useful in the CHR implementation of our algorithm.

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Section: Resultsmentioning

confidence: 99%

Section: •Xmentioning

confidence: 99%

Section: Chr Rulesmentioning

confidence: 99%

Section: Chr Rulesmentioning

confidence: 99%

See 2 more Smart Citations

Toward a first-order extension of Prolog's unification using CHR

Djelloul

Dao²,

Fruehwirth

2007

Proceedings of the 2007 ACM Symposium on Applied Computing

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“…Future work aims to reach a linear complexity solver by combining both the RT solver and our reachability computation with the union-find algorithm in CHR [13,4].…”

Section: Resultsmentioning

confidence: 99%

Complexity of a CHR Solver for Existentially Quantified Conjunctions of Equations over Trees

Meister

Djelloul

Frühwirth

Lecture Notes in Computer Science

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To cite this version:Abstract. Constraint Handling Rules (CHR) is a concurrent, committed-choice, rule-based language. One of the first CHR programs is the classic constraint solver for syntactic equality of rational trees that performs unification. We first prove its exponential complexity in time and space for non-flat equations and deduce from this proof a quadratic complexity for flat equations. We then present an extended CHR solver for solving existentially quantified conjunctions of non-flat equations in the theory of finite or infinite trees. We reach a quadratic complexity by first flattening the equations and introducing new existentially quantified variables, then using the classic solver, and finally eliminating particular equations and quantified variables.

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Complete Propagation Rules for Lexicographic Order Constraints over Arbitrary Domains

Frühwirth

2006

Lecture Notes in Computer Science

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Abstract. We give an efficiently executable specification of the global constraint of lexicographic order in the Constraint Handling Rules (CHR) language. In contrast to previous approaches, the implementation is short and concise without giving up on the best known worst case time complexity. It is incremental and concurrent by nature of CHR. It is provably correct and confluent. It is independent of the underlying constraint system, and therefore not restricted to finite domains. We have found a direct recursive decomposition of the problem. We also show completeness of constraint propagation, i.e. that all possible logical consequences of the constraint are generated by the implementation. Finally, we report about some practical implementation experiments.

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Parallelizing Union-Find in Constraint Handling Rules Using Confluence Analysis

Cited by 20 publications

References 15 publications

Toward a first-order extension of Prolog's unification using CHR

Toward a first-order extension of Prolog's unification using CHR

Complexity of a CHR Solver for Existentially Quantified Conjunctions of Equations over Trees

Complete Propagation Rules for Lexicographic Order Constraints over Arbitrary Domains

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