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@inproceedings{1649416,
author = {Bendík, Jaroslav and Meel, Kuldeep S.},
address = {Neuveden},
booktitle = {Computer Aided Verification - 32nd International Conference, CAV 2020},
doi = {http://dx.doi.org/10.1007/978-3-030-53288-8_21},
editor = {Shuvendu K. Lahiri and Chao Wang},
keywords = {minimal unsatisfiable subsets;MUS counting;diagnosis;metrics;knowledge base},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Neuveden},
isbn = {978-3-030-53287-1},
pages = {439-462},
publisher = {Springer, Cham},
title = {Approximate Counting of Minimal Unsatisfiable Subsets},
year = {2020}
}
TY - JOUR
ID - 1649416
AU - Bendík, Jaroslav - Meel, Kuldeep S.
PY - 2020
TI - Approximate Counting of Minimal Unsatisfiable Subsets
PB - Springer, Cham
CY - Neuveden
SN - 9783030532871
KW - minimal unsatisfiable subsets;MUS counting;diagnosis;metrics;knowledge base
N2 - Given an unsatisfiable formula F in CNF, i.e. a set of clauses, the problem of Minimal Unsatisfiable Subset (MUS) seeks to identify the minimal subset of clauses N subset F such that N is unsatisfiable. The emerging viewpoint of MUSes as the root causes of unsatisfiability has led MUSes to find applications in a wide variety of diagnostic approaches. Recent advances in finding and enumeration of MUSes have motivated researchers to discover applications that can benefit from rich information about the set of MUSes. One such extension is that of counting the number of MUSes, which has shown to describe the inconsistency metrics for general propositional knowledge bases. The current best approach for MUS counting is to employ a MUS enumeration algorithm, which often does not scale for the cases with a reasonably large number of MUSes. Motivated by the success of hashing-based techniques in the context of model counting, we design the first approximate counting procedure with (epsilon,delta) guarantees, called AMUSIC. Our approach avoids exhaustive MUS enumeration by combining the classical technique of universal hashing with advances in QBF solvers along with a novel usage of union and intersection of MUSes to achieve runtime efficiency. Our prototype implementation of AMUSIC is shown to scale to instances that were clearly beyond the reach of enumeration-based approaches.
ER -
BENDÍK, Jaroslav and Kuldeep S. MEEL. Approximate Counting of Minimal Unsatisfiable Subsets. In Shuvendu K. Lahiri and Chao Wang. \textit{Computer Aided Verification - 32nd International Conference, CAV 2020}. Neuveden: Springer, Cham, 2020, p.~439-462. ISBN~978-3-030-53287-1. Available from: https://dx.doi.org/10.1007/978-3-030-53288-8\_{}21.
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