Abstract
We extend the setting of Satisfiability Modulo Theories (SMT) by introducing a theory of costs \({\mathcal{C}}\), where it is possible to model and reason about resource consumption and multiple cost functions, e.g., battery, time, and space. We define a decision procedure that has all the features required for the integration withint the lazy SMT schema: incrementality, backtrackability, construction of conflict sets, and deduction. This naturally results in an SMT solver for the disjoint union of \({\mathcal{C}}\) and any other theory \({\mathcal{T}}\).
This framework has two important applications. First, we tackle the problem of Optimization Modulo Theories: rather than checking the existence of a satisfying assignment, as in SMT, we require a satisfying assignment that minimizes a given cost function. We build on the decision problem for SMT with costs, i.e., finding a satisfying assigniment with cost within an admissibility range, and propose two algorithms for optimization. Second, we use multiple cost functions to deal with PseudoBoolean constraints. Within the \({\text{SMT}({\mathcal C})}\) framework, the effectively PseudoBoolean constraints are dealt with by the cost solver, while the other constraints are reduced to pure boolean reasoning.
We implemented the proposed approach within the MathSAT SMT solver, and we experimentally evaluated it on a large set of benchmarks, also from industrial applications. The results clearly demonstrate the potential of the approach.
A. Cimatti is supported in part by the European Commission FP7-2007-IST-1-217069 COCONUT. A. Franzén, A. Griggio and R. Sebastiani are supported in part by SRC under GRC Custom Research Project 2009-TJ-1880 WOLFLING, and by MIUR under PRIN project 20079E5KM8_002.
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Cimatti, A., Franzén, A., Griggio, A., Sebastiani, R., Stenico, C. (2010). Satisfiability Modulo the Theory of Costs: Foundations and Applications. In: Esparza, J., Majumdar, R. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2010. Lecture Notes in Computer Science, vol 6015. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12002-2_8
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