Abstract
Explaining the causes of infeasibility of formulas has practical applications in various fields, such as artificial intelligence and formal verification. A minimal unsatisfiable core provides a succinct explanation of infeasibility and is valuable for applications. The problem of deriving minimal unsatisfiable cores from Boolean formulas has been addressed rather frequently in recent years. However little attention has been concentrated on extraction of the first-order unsatisfiable subformulas. In this paper, we present DFS-Finder, which finds minimal unsatisfiable cores in first-order logic, adopting a heuristic depth-first-search strategy. We demonstrate the effectiveness of this approach on a very extensive test of SMT-LIB benchmarks.
This work is supported by the National Natural Science Foundation of China under grant No.61070132.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Jorg, H., Ri, B.: Conformant planning via heuristic forward search: A new approach. Artificial Intelligence 170, 507–541 (2006)
Jain, H., Kroening, D.: Word level predicate abstraction and refinement for verifying RTL Verilog. In: Proceedings of the 42nd Design Automation Conference (DAC 2005), pp. 445–450 (2005)
Simmonds, J., et al.: Exploiting resolution proofs to speed up LTL vacuity detection for BMC. In: Proceedings of the 7th International Conference on Formal Methods in Computer Aided Design (FMCAD 2007), pp. 3–12 (2007)
Oh, Y., Mneimneh, M.N., Andraus, Z.S., Sakallah, K.A., Markov, I.L.: AMUSE: a minimally-unsatisfiable subformula extractor. In: Proceedings of the 41st Design Automation Conference (DAC 2004), pp. 518–523 (2004)
Lynce, I., Marques-Silva, J.P.: On computing minimum unsatisfiable cores. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 305–310. Springer, Heidelberg (2004)
Liffiton, M.H., Sakallah, K.A.: On finding all minimally unsatisfiable subformulas. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 173–186. Springer, Heidelberg (2005)
Gershman, R., Koifman, M., Strichman, O.: Deriving small unsatisfiable cores with dominators. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 109–122. Springer, Heidelberg (2006)
Gregoire, E., Mazuer, B., Piette, C.: Boosting a complete technique to find MSS and MUS thanks to a local search oracle. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 2300–2305 (2007)
van Maaren, H., Wieringa, S.: Finding guaranteed mUSes fast. In: Büning, K.H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 291–304. Springer, Heidelberg (2008)
Liffiton, M.H., Mneimneh, M.N., Lynce, I., Andraus, Z.S., Marques-Silva, J.P., Sakallah, K.A.: A branch and bound algorithm for extracting smallest minimal unsatisfiable formulas. Constraints 14(4), 415–442 (2009)
Piette, C., Hamadi, Y., Saïs, L.: Efficient combination of decision procedures for MUS computation. In: Ghilardi, S., Sebastiani, R. (eds.) FroCoS 2009. LNCS, vol. 5749, pp. 335–349. Springer, Heidelberg (2009)
Nadel, A.: Boosting minimal unsatisfiable core extraction. In: Proceedings of the 10th International Conference on Formal Methods in Computer Aided Design (FMCAD 2010), pp. 221–229 (2010)
Barrett, C.W., Berezin, S.: CVC Lite: A New Implementation of the Cooperating Validity Checker Category B. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 515–518. Springer, Heidelberg (2004)
Bozzano, M., Bruttomesso, R., Cimatti, A., Junttila, T., van Rossum, P., Schulz, S., Sebastiani, R.: An incremental and Layered Procedure for the Satisfiability of Linear Arithmetic Logic. In: Halbwachs, N., Zuck, L. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 317–333. Springer, Heidelberg (2005)
Dutertre, B., de Moura, L.: A Fast Linear-Arithmetic Solver for DPLL(T). In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 81–94. Springer, Heidelberg (2006)
Cimatti, A., Griggio, A., Sebastiani, R.: A simple and flexible way of computing small unsatisfiable cores in SAT modulo theories. In: Marques-Silva, J., Sakallah, K. (eds.) SAT 2007. LNCS, vol. 4501, pp. 334–339. Springer, Heidelberg (2007)
Marić, F., Janičić, P.: argo-lib: A generic platform for decision procedures. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 213–217. Springer, Heidelberg (2004)
Barret, C., Deters, M., Oliveras, A., et al.: http://www.smtcomp.org/2010/bench-marks.shtml (accessed in 2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, J. et al. (2011). Finding First-Order Minimal Unsatisfiable Cores with a Heuristic Depth-First-Search Algorithm. In: Yin, H., Wang, W., Rayward-Smith, V. (eds) Intelligent Data Engineering and Automated Learning - IDEAL 2011. IDEAL 2011. Lecture Notes in Computer Science, vol 6936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23878-9_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-23878-9_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23877-2
Online ISBN: 978-3-642-23878-9
eBook Packages: Computer ScienceComputer Science (R0)