The eXtended Least Number Heuristic

Abstract

This paper presents an algorithm, XLNH, to generate finite models of first order equational theories. Unlike conventional methods, which focus on using as few individual constants as possible to preserve symmetries, XLNH heuristically selects then fully generates the functions that appear in the problem, using a weighted directed graph of functional dependency. One key issue here is to constructively generate isomorphic partial models then further exploit the resulting symmetries. This algorithm proves very efficient on problems involving a unary bijective function f (like the additive inverse in a group or ring theory). When such a bijection is fully instantiated, XLNH statically exploits remaining isomorphic subspaces. These ideas are implemented using the public domain SEM software framework, and give order of magnitude improvements on many problems. These results are interesting on their own but potentially generalize to many practical CSP applications.