Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andraus Z S, Liffiton M H, Sakallah K A. Reveal: a formal verification tool for verilog designs. In: Proceedings of International Conference on Logic for Programming Artificial Intelligence and Reasoning, 2008. 343–352
Banda M G D L, Stuckey P J, Wazny J. Finding all minimal unsatisfiable subsets. In: Proceedings of International ACM Sigplan Conference on Principles and Practice of Declarative Programming, Uppsala, 2003. 32–43
Tong Y X, Chen L, Zhou Z M, et al. SLADE: a smart large-scale task decomposer in crowdsourcing. IEEE Trans Knowl Data Eng, 2018, 30: 1588–1601
Janota M, Marques-Silva J. cmMUS: a tool for circumscription-based mus membership testing. In: Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning, 2011. 266–271
Luo J, Li W. An algorithm to compute maximal contractions for Horn clauses. Sci China Inf Sci, 2011, 54: 244–257
Luo J. A general framework for computing maximal contractions. Front Comput Sci, 2013, 7: 83–94
Jiang D C, Li W, Luo J, et al. A decomposition based algorithm for maximal contractions. Front Comput Sci, 2013, 7: 801–811
Papadimitriou C H, Wolfe D. The complexity of facets resolved. J Comput Syst Sci, 1988, 37: 2–13
Bacchus F, Katsirelos G. Finding a collection of MUSes incrementally. In: Integration of AI and OR Techniques in Constraint Programming. Berlin: Springer, 2016. 35–44
Ryvchin V, Strichman O. Faster extraction of high-level minimal unsatisfiable cores. In: Proceedings of International Conference on Theory and Applications of Satisfiability Testing, Ann Arbor, 2011. 174–187
Xiao G H, Ma Y. Inconsistency measurement based on variables in minimal unsatisfiable subsets. In: Proceedings of the 20th European Conference on Artificial Intelligence, Montpellier, 2012
Hou A M. A theory of measurement in diagnosis from first principles. Artif Intell, 1994, 65: 281–328
Bailey J, Stuckey P J. Discovery of minimal unsatisfiable subsets of constraints using hitting set dualization. In: Proceedings of International Workshop on Practical Aspects of Declarative Languages, 2005. 174–186
Liffiton M H, Sakallah K A. Algorithms for computing minimal unsatisfiable subsets of constraints. J Autom Reason, 2008, 40: 1–33
Stern R, Kalech M, Feldman A, et al. Exploring the duality in conflict-directed model-based diagnosis. In: Proceedings of the 26th AAAI Conference on Artificial Intelligence, Toronto, 2012
Liffiton M H, Previti A, Malik A, et al. Fast, flexible MUS enumeration. Constraints, 2016, 21: 223–250
Previti A, Marques-Silva J. Partial MUS enumeration. In: Proceedings of the 27th AAAI Conference on Artificial Intelligence, 2013
Kahng A B, Lienig J, Markov I L, et al. VLSI Physical Design: From Graph Partitioning to Timing Closure. Berlin: Springer, 2011
Schloegel K, Karypis G, Kumar V. Graph partitioning for high-performance scientific simulations. In: Sourcebook of Parallel Computing. San Francisco: Morgan Kaufmann Publishers, 2003. 491–541
Newman M. Networks: An Introduction. Oxford: Oxford University Press, 2010
Blondel V D, Guillaume J L, Lambiotte R, et al. Fast unfolding of communities in large networks. J Stat Mech, 2008, 2008: 10008
Newman M E J, Girvan M. Finding and evaluating community structure in networks. Phys Rev E, 2004, 69: 026113
Newman M E J. Modularity and community structure in networks. Proc Natl Acad Sci USA, 2006, 103: 8577–8582
Acknowledgements
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).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11432-019-9881-0