On Local Domain Symmetry for Model Expansion

TL;DR

This paper develops methods to detect and break local domain symmetries in model expansion problems, improving automation and efficiency in symmetry handling within logic-based systems.

Contribution

It introduces sufficient conditions for symmetry, identifies local domain interchangeability, and provides efficient detection algorithms, advancing symmetry exploitation in model expansion.

Findings

Effective symmetry detection algorithms developed

Complete symmetry breaking often achievable for local domain interchangeability

Experimental results show strengths and limitations compared to SBASS

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 on local 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 of local 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 to SBASS , a symmetry breaking technique for answer set programming.