On the computation of local interchangeability in discrete constraint satisfaction problems

In. [4], Freuder defines several types of interchangeability to capture the equivalence among the values of a variable in a discrete constraint satisfaction problem (CSP), and provides a procedure for computing one type of local interchangeability. In this paper, we first extend this procedure for computing a weak form of local interchangeability. Second, we show that the modified procedure can be used to generate a conjunctive decomposition of the CSP by localizing, in the CSP, independent subproblems. Third, for the case of constraints of mutual exclusion, we show that locally Interchangeable values can be computed in a straightforward manner, and that the only possible type of ~ocal interchangeability is the one that induces locally Independent subproblems. Finally, we give hints on how to exploit these results in practice, establish a lattice that relates some types of interchangeability, and identify directions for future research.