A Note on Symmetry Heuristics in SEM

Abstract

We analyse two symmetry heuristics, i.e. heuristics that reduce the search space through properties of symmetry, in the finite model generator SEM. These are SEM’s original LNH, and a recent extension XLNH. Our aim is to show how a simple group-theoretic framework brings much clarity in this matter, especially through group actions. Both heuristics can be seen as computationally efficient ways of applying a general symmetry pruning theorem. Moreover, simple combinatorics provide some insight into the relative performances of these heuristics. We finally expose a fundamental difficulty in making SEM symmetry efficient by symmetry pruning.