On local domain symmetry for model expansion
Jo Devriendt, Bart Bogaerts, Maurice Bruynooghe, Marc Denecker · Theory and Practice of Logic Programming · 2016
Abstract Symmetry in combinatorial problems is an extensively studied topic. We continue this research in the context of model expansion problems, with the aim of automating the workflow of detecting and breaking symmetry. We focus onlocal domain symmetry, which is induced by permutations of domain elements, and which can be detected on a first-order level. As such, our work is a continuation of the symmetry exploitation techniques of model generation systems, while it differs from more recent symmetry breaking techniques in answer set programming which detect symmetry on ground programs. Our main contributions are sufficient conditions for symmetry of model expansion problems, the identification oflocal domain interchangeability, which can often be broken completely, and efficient symmetry detection algorithms for both local domain interchangeability as well as local domain symmetry in general. Our approach is implemented in the model expansion system IDP, and we present experimental results showcasing the strong and weak points of our approach compared tosbass, a symmetry breaking technique for answer set programming.