The problem of finding minimal unsatisfiable subsets (MUSes) has been studied frequently because of its theoretical importance and wide range of applications in domains such as electronic design automation, software, and integrated circuit verification. In this paper, a method for accelerating the enumeration of MUSes based on inconsistency graph partitioning is proposed. First, an inconsistency graph of a set of clauses is constructed by extracting the inconsistency relations between literals of different clauses. In this paper, we show that by partitioning the inconsistency graph into small connected components through a vertex cut, the enumeration of MUSes in different components becomes independent and it is possible to compute them separately. Moreover, the MUSes of the original clause set can be constructed by merging the unit clauses in the MUSes of these connected components back into the clauses in the vertex cut. Experiments show that by integrating the acceleration method into the MARCO MUSes enumerator, there is a 2–3 times improvement in the average runtime of solved instances for randomly generated benchmarks. By integrating the acceleration method into itself as an MUS enumerator, there is another 3–4 times improvement when compared with the accelerated MARCO.
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This work was supported by National Natural Science Foundation of China (Grant Nos. 61690202, 61502022) and State Key Laboratory of Software Development Environment (Grant No. SKLSDE-2017ZX-17).
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Luo, J., Liu, S. Accelerating MUS enumeration by inconsistency graph partitioning. Sci. China Inf. Sci. 62, 212104 (2019). https://doi.org/10.1007/s11432-019-9881-0
- minimal unsatisfiable subsets
- inconsistency graph
- graph partition