An open-ended finite domain constraint solver

Abstract

We describe the design and implementation of a finite domain constraint solver embedded in a Prolog system using an extended unification mechanism via attributed variables as a generic constraint interface. The solver is essentially a scheduler for indexicals, i.e. reactive functional rules encoding local consistency methods performing incremental constraint solving or entailment checking, and global constraints, i.e. general propagators which may use specialized algorithms to achieve a higher degree of consistency or better time and space complexity. The solver has an open-ended design: the user can introduce new constraints, either in terms of indexicals by writing rules in a functional notation, or as global constraints via a Prolog programming interface. Constraints defined in terms of indexicals can be linked to 0/1-variables modeling entailment; thus indexicals are used for constraint solving as well as for entailment testing. Constraints can be arbitrarily combined using the propositional connectives by automatic expansion to systems of reified constraints.

On Generators of Random Quasigroup Problems

“…We have implemented the presented generators using the clpfd library [3] of SICStus Prolog version 3.11.2. All presented results were accomplished under Windows XP Professional on 1.8 GHz Pentium 4 with 512 MB RAM.…”

“…Then the diameter of the new graph and hence the minimal distance between any two (proper or improper) nodes is bounded by 2(N-1) 3 (for a formal proof see [9]). They represent the Latin square of order N by a contingency table f of size N×N×N that contains {0,1} values only.…”

Perfect Derived Propagators

“…Views are related to indexicals [2,10], propagators that prune a single variable and are defined over range expressions. However, views are not used to define propagators, but to derive new propagators from existing ones.…”

Towards Solver-Independent Propagators

“…In a nutshell, an indexical defines a restriction on the domain of a decision variable, given the current domains of other decision variables. Indexicals have been used to implement user-defined constraints in various finite-domain systems, such as SICStus Prolog [6]. While indexicals can originally only deal with constraints of fixed arity, we extend them to deal with constraints of non-fixed arity (often referred to as global constraints) by handling arrays of decision variables and operations on such arrays (iteration and n-ary operators).…”