Abstract
dpll(t) is a central algorithm for Satisfiability Modulo Theories (smt) solvers. The algorithm combines results of reasoning about the Boolean structure of a formula with reasoning about conjunctions of theory facts to decide satisfiability. This architecture enables modern solvers to combine the performance benefits of propositional satisfiability solvers and conjunctive theory solvers. We characterise dpll(t) as an abstract interpretation algorithm that computes a product of two abstractions. Our characterisation allows a new understanding of dpll(t) as an instance of an abstract procedure to combine reasoning engines beyond propositional solvers and conjunctive theory solvers. In addition, we show theoretically that the split into Boolean and theory reasoning is sometimes unnecessary and demonstrate empirically that it can be detrimental to performance.
Supported by the Toyota Motor Corporation, ERC project 280053, EPSRC project EP/J012564/1, and the FP7 STREP PINCETTE.
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
Badban, B., van de Pol, J., Tveretina, O., Zantema, H.: Generalizing DPLL and satisfiability for equalities. Inf. Comput. 205(8) (2007)
Barrett, C., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Splitting on Demand in SAT Modulo Theories. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 512–526. Springer, Heidelberg (2006)
Barrett, C.W., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Handbook of Satisfiability. IOS Press (2009)
Cotton, S.: Natural Domain SMT: A Preliminary Assessment. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 77–91. Springer, Heidelberg (2010)
Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: POPL (1979)
Cousot, P., Cousot, R., Mauborgne, L.: The Reduced Product of Abstract Domains and the Combination of Decision Procedures. In: Hofmann, M. (ed.) FOSSACS 2011. LNCS, vol. 6604, pp. 456–472. Springer, Heidelberg (2011)
D’Silva, V., Haller, L., Kroening, D.: Satisfiability Solvers Are Static Analysers. In: Miné, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol. 7460, pp. 317–333. Springer, Heidelberg (2012)
D’Silva, V., Haller, L., Kroening, D.: Abstract Conflict Driven Clause Learning. In: POPL (to apppear, 2013)
D’Silva, V., Haller, L., Kroening, D., Tautschnig, M.: Numeric Bounds Analysis with Conflict-Driven Learning. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 48–63. Springer, Heidelberg (2012)
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)
Fränzle, M., Herde, C., Teige, T., Ratschan, S., Schubert, T.: Efficient solving of large non-linear arithmetic constraint systems with complex Boolean structure. JSAT 1(3-4) (2007)
Ganzinger, H., Hagen, G., Nieuwenhuis, R., Oliveras, A., Tinelli, C.: DPLL(T): Fast Decision Procedures. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 175–188. Springer, Heidelberg (2004)
Griggio, A.: A Practical Approach to Satisfiability Modulo Linear Integer Arithmetic. JSATÂ 8 (2012)
Haller, L., Griggio, A., Brain, M., Kroening, D.: Deciding floating-point logic with systematic abstraction. In: FMCAD (2012)
Harris, W.R., Sankaranarayanan, S., Ivančić, F., Gupta, A.: Program analysis via satisfiability modulo path programs. In: POPL (2010)
Jin, H., Somenzi, F.: Strong conflict analysis for propositional satisfiability. In: DATE (2006)
Jovanović, D., de Moura, L.: Cutting to the Chase Solving Linear Integer Arithmetic. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 338–353. Springer, Heidelberg (2011)
Jovanović, D., de Moura, L.: Solving Non-linear Arithmetic. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 339–354. Springer, Heidelberg (2012)
McMillan, K.L., Kuehlmann, A., Sagiv, M.: Generalizing DPLL to Richer Logics. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 462–476. Springer, Heidelberg (2009)
Nieuwenhuis, R., Oliveras, A.: DPLL(T) with Exhaustive Theory Propagation and Its Application to Difference Logic. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 321–334. Springer, Heidelberg (2005)
Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: From an abstract Davis–Putnam–Logemann–Loveland procedure to DPLL(T). JACM 53 (2006)
Thakur, A., Reps, T.: A Method for Symbolic Computation of Abstract Operations. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 174–192. Springer, Heidelberg (2012)
Thakur, A., Reps, T.: A Generalization of Stålmarck’s Method. In: Miné, A., Schmidt, D. (eds.) SAS 2012. LNCS, vol. 7460, pp. 334–351. Springer, Heidelberg (2012)
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
Brain, M., D’Silva, V., Haller, L., Griggio, A., Kroening, D. (2013). An Abstract Interpretation of DPLL(T). In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2013. Lecture Notes in Computer Science, vol 7737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35873-9_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-35873-9_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35872-2
Online ISBN: 978-3-642-35873-9
eBook Packages: Computer ScienceComputer Science (R0)