Incremental Information Interaction-Based Algorithm for Enumerating MUSes

Jiang Luyu; Ouyang Dantong; Zhang Qi; Tai Ran; Zhang Liming

doi:10.7544/issn1000-1239.202440326

Journal of Computer Research and Development > 2025 > 62(5): 1226-1234. > DOI: 10.7544/issn1000-1239.202440326 CSTR: 32373.14.issn1000-1239.202440326

Jiang Luyu, Ouyang Dantong, Zhang Qi, Tai Ran, Zhang Liming. Incremental Information Interaction-Based Algorithm for Enumerating MUSes[J]. Journal of Computer Research and Development, 2025, 62(5): 1226-1234. DOI: 10.7544/issn1000-1239.202440326

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Incremental Information Interaction-Based Algorithm for Enumerating MUSes

College of Computer Science and Technology, Jilin University, Changchun 130012
Key Laboratory of Symbol Computation and Knowledge Engineering (Jilin University), Ministry of Education, Changchun 130012

Funds: This work was supported by the National Natural Science Foundation of China (62076108, 61872159) and the Scientific Research Project of Education Department of Jilin Province (JJKH20211106KJ, JJKH20211103KJ).

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Author Bio:
Jiang Luyu: born in 1998. PhD candidate. Student member of CCF. Her main research interests include SAT, combinatorial optimization, and model-based diagnosis problem

Ouyang Dantong: born in 1968. PhD, professor, PhD supervisor. Senior member of CCF. Her main research interests include automatic reasoning and model-based diagnosis problem. （ouyd@jlu.edu.cn）

Zhang Qi: born in 1998. PhD candidate. Student member of CCF. His main research interests include SAT and model-based diagnosis problem

Tai Ran: born in 1997. PhD candidate. Student member of CCF. His main research interests include combinatorial optimization and model-based diagnosis problem

Zhang Liming: born in 1980. PhD, senior engineer. Senior member of CCF. His main research interests include SAT and model-based diagnosis problem
Received Date: May 20, 2024
Revised Date: September 28, 2024
Accepted Date: October 14, 2024
Available Online: October 21, 2024

Graphical Abstract

Abstract

Abstract

Enumerating minimal unsatisfiable subsets (MUS) is an important issue in theoretical computer science. Given an unsatisfiable Boolean formula, the number of its MUS is exponentially related to the formula’s scale. Contemporary methods aim to identify MUSes as many as possible within appropriate time limits. Dealing with the huge search space and choosing a suitable node to expand can markedly reduce the time consumption on shrink and grow operations, thereby the algorithm could obtain better performance. We introduce an incremental information interaction-based MUS solving algorithm, denoted as MARCO-MSS4MUS, which utilizes the duality and complementary relationships among MUS, minimal correction set (MCS), and maximal satisfiable subset (MSS). Based on the framework of MARCO algorithm, the proposed algorithm selects a more suitable node to expand via intersection and union information of previously identified MSSes during the search, i.e., the incremental MSS information is employed as a heuristic for node selection to accelerate the enumeration of MUS. This process also benefits in identifying more MSSes, in turn, the incremental MSS information helps select a better node for next exploration, thereby achieving an interaction of incremental information. Two theorems and two corollaries regarding interactive incremental information are proposed and the feasibility of our MARCO-MSS4MUS algorithm is theoretically analyzed. Experiments on standard MUS benchmark instances show the superiority of the proposed algorithm over state-of-the-art algorithms. Both the enumeration efficiency and the number of enumerated wins of the proposed algorithm are significantly improved compared with existing algorithms.
- minimal unsatisfiable subset (MUS),
- maximal satisfiable subset (MSS),
- infeasibility analysis,
- hitting set,
- duality

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References (28)

References

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