, Volume 10, Issue 4, pp 339-362

First online:

Reformulation of Global Constraints Based on Constraints Checkers

  • Nicolas BeldiceanuAffiliated withLINA FRE CNRS 2729, École des Mines de Nantes Email author 
  • , Mats CarlssonAffiliated withSICS
  • , Romuald DebruyneAffiliated withLINA FRE CNRS 2729, École des Mines de Nantes
  • , Thierry PetitAffiliated withLINA FRE CNRS 2729, École des Mines de Nantes

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This article deals with global constraints for which the set of solutions can be recognized by an extended finite automaton whose size is bounded by a polynomial in n, where n is the number of variables of the corresponding global constraint. By reducing the automaton to a conjunction of signature and transition constraints we show how to systematically obtain an automaton reformulation. Under some restrictions on the signature and transition constraints, this reformulation maintains arc-consistency. An implementation based on some constraints as well as on the metaprogramming facilities of SICStus Prolog is available. For a restricted class of automata we provide an automaton reformulation for the relaxed case, where the violation cost is the minimum number of variables to unassign in order to get back to a solution.


global constraints automata reformulation