Complexity of a CHR solver for existentially quantified conjunctions of equations over trees

Authors:
Marc Meister;Khalil Djelloul;Thom Frühwirth
Affiliations:
Fakultät für Ingenieurwissenschaften und Informatik, Universität Ulm, Germany;Fakultät für Ingenieurwissenschaften und Informatik, Universität Ulm, Germany;Fakultät für Ingenieurwissenschaften und Informatik, Universität Ulm, Germany
Venue:
CSCLP'06 Proceedings of the constraint solving and contraint logic programming 11th annual ERCIM international conference on Recent advances in constraints
Year:
2006

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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.