An ASP-Based Framework for MUSes
This work addresses the need to understand core reasons for unsatisfiability in applications like verification and debugging, but it is incremental as it builds on existing MUS enumeration methods with a new computational approach.
The paper tackles the problem of enumerating minimal unsatisfiable subsets (MUSes) for unsatisfiable formulas by introducing MUS-ASP, an answer set programming-based framework. The result shows that MUS-ASP accelerates MUS enumeration and counting tasks, particularly when integrated with hybrid solvers.
Given an unsatisfiable formula, understanding the core reason for unsatisfiability is crucial in several applications. One effective way to capture this is through the minimal unsatisfiable subset (MUS), the subset-minimal set of clauses that remains unsatisfiable. Current research broadly focuses on two directions: (i) enumerating as many MUSes as possible within a given time limit, and (ii) counting the total number of MUSes for a given unsatisfiable formula. In this paper, we introduce an answer set programming-based framework, named MUS-ASP, designed for online enumeration of MUSes. ASP is a powerful tool for its strengths in knowledge representation and is particularly suitable for specifying complex combinatorial problems. By translating MUS enumeration into answer set solving, MUS-ASP leverages the computational efficiency of state-of-the-art ASP systems. Our extensive experimental evaluation demonstrates the effectiveness of MUS-ASP and highlights the acceleration in both MUS enumeration and counting tasks, particularly when integrated within hybrid solvers, including the framework proposed in this paper.