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

Marc Meister (1) , Khalil Djelloul (2) , Thom Fruehwirth (1)

1 Universität Ulm - Ulm University [Ulm, Allemagne]
2 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

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.

Domaines: Logique en informatique [cs.LO]

Marc Meister, Khalil Djelloul, Thom Fruehwirth. Complexity of a CHR solver for existentially quantified conjunctions of equations over trees.. Recent advances in constraints Lecture notes in computer science. Revised selected paper csclp 2006., Apr 2007, France. pp.LNAI, Vol 4651. P 139-153. ⟨hal-00202313⟩