Constraint Problem Specification as Compression

A theme of Algorithmic Information Theory is that, for any scientific or mathematical theory, “understanding is compression”. That is, the more compactly we can express a theory, the more comprehensible it becomes. We apply this philosophy to the problem of constraint problem specification. Instead of defining a new specification language, we use Constraint Logic Programming as a meta-language to describe itself compactly via compression techniques. We show that this approach can produce short, clear descriptions of standard constraint problems. In particular, it allows a simple and natural description of compound variables and channeling constraints. Moreover, for problems whose specification requires the solution of an auxiliary problem, a single specification can unify the two problems. We call our specification language Kolmogorov.