Exploiting Symmetries in MUS Computation (Extended version)
This work addresses a bottleneck in eXplainable Constraint Solving for users needing explanations of unsatisfiable constraints, though it is incremental as it adapts known techniques to an understudied setting.
The paper tackles the computational expense of finding Minimal Unsatisfiable Subsets (MUSes) in symmetric constraint problems by adapting existing MUS-computation methods to exploit symmetries, resulting in a significant reduction in runtime compared to baseline methods.
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.