Abstract

Constraint satisfaction problems (CSP) or Boolean satisfiability problem (SAT) are two well-known paradigms to model and solve combinatorial problems. Modeling and resolution of CSP is often strengthened by global constraints (e.g., Alldiff constraint). This paper highlights two different ways of handling specific structural information: a uniform propagation framework to handle (interleaved) Alldiff constraints with some CSP reduction rules and a SAT encoding of these rules that preserves the reduction properties of CSP. We illustrate our approach on the well-known Sudoku puzzle which presents 27 overlapping Alldiff constraints in its 9 × 9 standard size. We also present some preliminary results we obtained in CHR, GeCode and Zchaff.

Key words: Boolean satisfiability problem (SAT), computer science, decision support, constraint programming, global constraint, automated reasoning.