Exploiting Symmetries in MUS Computation (Extended version)

TL;DR

This paper introduces methods to leverage symmetries in the computation of Minimal Unsatisfiable Subsets (MUSes) within constraint solving, significantly reducing runtime on symmetric problems.

Contribution

It adapts existing symmetry-handling techniques to MUS computation, addressing a gap in symmetry exploitation for unsatisfiable constraint problems.

Findings

Significant runtime reduction on symmetric problems

Effective adaptation of symmetry techniques to MUS algorithms

Enhanced efficiency in explainable constraint solving

Abstract

In eXplainable Constraint Solving (XCS), it is common to extract a Minimal Unsatisfiable Subset (MUS) from a set of unsatisfiable constraints. This helps explain to a user why a constraint specification does not admit a solution. Finding MUSes can be computationally expensive for highly symmetric problems, as many combinations of constraints need to be considered. In the traditional context of solving satisfaction problems, symmetry has been well studied, and effective ways to detect and exploit symmetries during the search exist. However, in the setting of finding MUSes of unsatisfiable constraint programs, symmetries are understudied. In this paper, we take inspiration from existing symmetry-handling techniques and adapt well-known MUS-computation methods to exploit symmetries in the specification, speeding-up overall computation time. Our results display a significant reduction of runtime for our adapted algorithms compared to the baseline on symmetric problems.