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Software Engineering Research, Management and Applications pp 231–246Cite as

Solving SMT Problems with a Costly Decision Procedure by Finding Minimum Satisfying Assignments of Boolean Formulas

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Part of the Studies in Computational Intelligence book series (SCI,volume 496)

Abstract

An SMT-solving procedure can be implemented by using a SAT solver to find a satisfying assignment of the propositional skeleton of the predicate formula and then deciding the feasibility of the assignment using a particular decision procedure. The complexity of the decision procedure depends on the size of the assignment. In case that the runtime of the solving is dominated by the decision procedure it is convenient to find short satisfying assignments in the SAT solving phase. Unfortunately most of the modern state-of-the-art SAT solvers always output a complete assignment of variables for satisfiable formulas even if they can be satisfied by assigning truth values to only a fraction of the variables. In this paper,we first describe an application in the code performance modeling domain, which requires SMT-solving with a costly decision procedure. Then we focus on the problem of finding minimum-size satisfying partial truth assignments. We describe and experimentally evaluate several methods how to solve this problem. These include reduction to partial maximum satisfiability - PMaxSAT, PMinSAT, pseudo-Boolean optimization and iterated SAT solving. We examine the methods experimentally on existing benchmark formulas as well as on a new benchmark set based on the performance modeling scenario.

Keywords

  • Decision Procedure
  • Conjunctive Normal Form
  • Truth Assignment
  • Cardinality Constraint
  • Satisfying Assignment

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  1. Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 2/25, 118 00, Prague, Czech Republic

    Martin Babka & Tomáš Balyo

  2. Department of Distributed and Dependable Systems, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 2/25, 118 00, Prague, Czech Republic

    Jaroslav Keznikl

  3. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou veží 2, 182 07, Prague, Czech Republic

    Jaroslav Keznikl

Authors
  1. Martin Babka
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  2. Tomáš Balyo
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  3. Jaroslav Keznikl
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Correspondence to Martin Babka .

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Editors and Affiliations

  1. , Software Engineering & Information, Central Michigan University, Mt. Pleasant, 48859, Michigan, USA

    Roger Lee

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Babka, M., Balyo, T., Keznikl, J. (2014). Solving SMT Problems with a Costly Decision Procedure by Finding Minimum Satisfying Assignments of Boolean Formulas. In: Lee, R. (eds) Software Engineering Research, Management and Applications. Studies in Computational Intelligence, vol 496. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00948-3_15

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  • DOI: https://doi.org/10.1007/978-3-319-00948-3_15

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