Abstract
SMT-based applications increasingly rely on SMT solvers being able to deal with quantified formulas. Current work shows that for formulas with quantifiers over uninterpreted sorts counter-models can be obtained by integrating a finite model finding capability into the architecture of a modern SMT solver. We examine various strategies for on-demand quantifier instantiation in this setting. Here, completeness can be achieved by considering all ground instances over the finite domain of each quantifier. However, exhaustive instantiation quickly becomes unfeasible with larger domain sizes. We propose instantiation strategies to identify and consider only a selection of ground instances that suffices to determine the satisfiability of the input formula. We also examine heuristic quantifier instantiation techniques such as E-matching for the purpose of accelerating the search. We give experimental evidence that our approach is practical for use in industrial applications and is competitive with other approaches.
The work of the first two authors was partially funded by a grant from Intel Corporation.
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.
References
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press (1998)
Baumgartner, P., Tinelli, C.: The Model Evolution calculus as a first-order DPLL method. Artificial Intelligence 172, 591–632 (2008)
de Moura, L., Bjørner, N.S.: Efficient E-matching for SMT solvers. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 183–198. Springer, Heidelberg (2007)
Blanchette, J.C.: Personal communication (2013)
Blanchette, J.C., Böhme, S., Paulson, L.C.: Extending Sledgehammer with SMT solvers. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 116–130. Springer, Heidelberg (2011)
Claessen, K., Sörensson, N.: New techniques that improve MACE-style finite model building. In: CADE-19 Workshop: Model Computation – Principles, Algorithms, Applications, pp. 11–27 (2003)
Ganzinger, H., Korovin, K.: New directions in instantiation-based theorem proving. In: Proceedings of LICS 2003, pp. 55–64. IEEE Computer Society (2003)
Ge, Y., de Moura, L.: Complete instantiation for quantified formulas in satisfiabiliby modulo theories. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 306–320. Springer, Heidelberg (2009)
Goel, A., Krstic, S., Tuttle, R.L.M.: SMT-based system verification with DVF. In: Proceedings of SMT 2012 (2012)
Jacobs, S.: Incremental instance generation in local reasoning. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 368–382. Springer, Heidelberg (2009)
Korovin, K.: iProver – an instantiation-based theorem prover for first-order logic (System description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 292–298. Springer, Heidelberg (2008)
Krstić, S., Goel, A.: Architecting solvers for SAT modulo theories: Nelson-Oppen with DPLL. In: Konev, B., Wolter, F. (eds.) FroCos 2007. LNCS (LNAI), vol. 4720, pp. 1–27. Springer, Heidelberg (2007)
Reynolds, A., Tinelli, C., Goel, A., Krstić, S.: Finite model finding in SMT. In: Proceedings of CAV 2013. LNCS. Springer (accepted, 2013)
Tuttle, M.R., Goel, A.: Protocol proof checking simplified with SMT. In: Proceedings of NCA 2012, pp. 195–202. IEEE Computer Society (2012)
Zhang, J., Zhang, H.: SEM: a system for enumerating models. In: Proceedings of IJCAI 1995, pp. 298–303 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Reynolds, A., Tinelli, C., Goel, A., Krstić, S., Deters, M., Barrett, C. (2013). Quantifier Instantiation Techniques for Finite Model Finding in SMT. In: Bonacina, M.P. (eds) Automated Deduction – CADE-24. CADE 2013. Lecture Notes in Computer Science(), vol 7898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38574-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-38574-2_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38573-5
Online ISBN: 978-3-642-38574-2
eBook Packages: Computer ScienceComputer Science (R0)