Reformulation of Global Constraints Based on Constraints Checkers

Abstract

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.

Sequencing and Counting with the multicost-regular Constraint

“…Coincidently, Pesant [1] and Beldiceanu et al [5] introduce two orthogonal approaches to achieve GAC on regular (see Figure 1). The approach proposed by Pesant [1] is to unfold Π as an acyclic DFA Π n which accepts only the words of length n. By construction, Π n is a layered multigraph with state s in layer 0 (the source), the accepting states A in layer n (the sinks), and where the set of arcs in any layer i coincides with δ i .…”

“…The paper is organized as follows. In Section 2, we present the class of regular constraints and provide a theoretical comparison between the pathfinding approach of Pesant [1] and the decomposition-based approach of Beldiceanu et al [5]. We introduce then the new constraint multicost-regular.…”

Focus : A Constraint for Concentrating High Costs

“…When X is a {N k ,P k }-sequence, for instance an instantiation I[X], and y c is fixed to a value v c , we can encode a checker for FOCUS, based on the computation of the focus cardinality of X. 1 The correctness of Algorithm 1 is proved by Properties 1 and 2. Its time complexity is obviously O(n).…”

“…We selected the paradigm presented in [1]. Under some conditions, this framework leads to a reformulation where a complete filtering is achieved, despite the counters.…”

“…The automaton has two states and two counters. The constraint network N (hypergraph) encoding the automaton [1] is not Berge-Acyclic [4]. Propagating directly the constraints in N does not necessarily entail a complete filtering.…”