Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

In various areas of computer science, e.g. requirements analysis, software development, or formal verification, we deal with a set of constraints/requirements. If the constraints cannot be satisfied simultaneously, it is desirable to identify the core problems among them. Such cores are called minimal unsatisfiable subsets (MUSes). The more MUSes are identified, the more information about the conflicts among the constraints is obtained. However, a full enumeration of all MUSes is in general intractable due to the combinatorial explosion. We therefore search for algorithms that enumerate MUSes in an online manner, i.e. algorithms that produce MUSes one by one and can be terminated anytime. Furthermore, as the list of constraint domains is quite long and new applications still arise, it is desirable to have algorithms that are applicable in arbitrary constraint domain. The problem of online MUS enumeration in a general constraint domains has been studied before and several algorithms were developed. However, the majority of these algorithms were evaluated only in the domain of Boolean logic. In this work, we provide a novel recursive algorithm for online MUS enumeration that is applicable to an arbitrary constraint domain and that outperforms the state-of-the-art algorithms. We evaluate the algorithm on a variety of benchmarks taken from three different constraint domains: Boolean constraints, SMT constraints, and LTL constraints.