Abstract
Much attention has been given in recent years to the problem of finding Minimally Unsatisfiable Subformulas (MUSes) of Boolean formulas. In this paper, we present a new view of the problem, strongly linking it to the maximal satisfiability problem. From this relationship, we have developed a novel technique for extracting all MUSes of a CNF formula, tightly integrat ing our implementation with a modern SAT solver. We also present another algorithm for finding all MUSes, developed independently but based on the same relationship. Experimental comparisons show that our approach is con sistently faster than the other, and we discuss ways in which ideas from both could be combined to improve further.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bailey, J., Stuckey, P.J.: Discovery of Minimal Unsatisfiable Subsets of Constraints Using Hitting Set Dualization. In: Hermenegildo, M.V., Cabeza, D. (eds.) PADL 2004. LNCS, vol. 3350, pp. 174–186. Springer, Heidelberg (2005)
de la Banda, M., Stuckey, P., Wazny, J.: Finding All Minimal Unsatisfiable Subsets. In: Proc. of the Fifth ACM-SIGPLAN International Conference on Principles and Practice of Declarative Programming (PPDP 2003), pp. 32–43 (2003)
Bruni, R., Sassano, A.: Restoring Satisfiability or Maintaining Unsatisfiability by Finding Small Unsatisfiable Subformulae. Electronic Notes in Discrete Mathematics 9 (2001)
Bruni, R.: Approximating Minimal Unsatisfiable Subformulae by Means of Adaptive Core Search. Discrete Applied Mathematics 130(2), 85–100 (2003)
Chinneck, J.W., Dravnieks, E.W.: Locating Minimal Infeasible Constraint Sets in Linear Programs. ORSA Journal on Computing 3(2), 157–168 (1991)
Eén, N., Sörensson, N.: An Extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Huang, J.: MUP: A Minimal Unsatisfiability Prover. In: Proc. of the Tenth Asia and South Pacific Design Automation Conference (ASP-DAC) (January 2005)
Karp, R.M.: Reducibility Among Combinatorial Problems. In: Proc. of a Symposium on the Complexity of Computer Computations, pp. 85–103 (1972)
Liffiton, M., Andraus, Z., Sakallah, K.: From Max-SAT to Min-UNSAT: Insights and Applications. Technical Report CSE-TR-506-05, University of Michigan (2005)
Oh, Y., Mneimneh, M., Andraus, Z., Sakallah, K., Markov, I.L.: AMUSE: A Minimally-Unsatisfiable Subformula Extractor. In: Proc. of the 41st Annual Conference on Design Automation, pp. 518–523. ACM Press, New York (2004)
SAT benchmarks from Automotive Product Configuration, http://www-sr.informatik.uni-tuebingen.de/~sinz/DC/
Sinz, C., Kaiser, A., Küchlin, W.: Formal Methods for the Validation of Automotive roduct Configuration Data. Artificial Intelligence for Engineering Design, Analysis and Manufacturing 17(1), 75–97 (2003)
Zhang, L., Malik, S.: Extracting small unsatisfiable cores from unsatisfiable Boolean formula. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liffiton, M.H., Sakallah, K.A. (2005). On Finding All Minimally Unsatisfiable Subformulas. In: Bacchus, F., Walsh, T. (eds) Theory and Applications of Satisfiability Testing. SAT 2005. Lecture Notes in Computer Science, vol 3569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499107_13
Download citation
DOI: https://doi.org/10.1007/11499107_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26276-3
Online ISBN: 978-3-540-31679-4
eBook Packages: Computer ScienceComputer Science (R0)