Abstraction-Based Satisfiability Solving of Presburger Arithmetic

  • Daniel Kroening
  • Joël Ouaknine
  • Sanjit A. Seshia
  • Ofer Strichman
Conference paper

DOI: 10.1007/978-3-540-27813-9_24

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3114)
Cite this paper as:
Kroening D., Ouaknine J., Seshia S.A., Strichman O. (2004) Abstraction-Based Satisfiability Solving of Presburger Arithmetic. In: Alur R., Peled D.A. (eds) Computer Aided Verification. CAV 2004. Lecture Notes in Computer Science, vol 3114. Springer, Berlin, Heidelberg

Abstract

We present a new abstraction-based framework for deciding satisfiability of quantifier-free Presburger arithmetic formulas. Given a Presburger formula φ, our algorithm invokes a SAT solver to produce proofs of unsatisfiability of approximations of φ. These proofs are in turn used to generate abstractions of φ as inputs to a theorem prover. The SAT-encodings of the approximations of φ are obtained by instantiating the variables of the formula over finite domains. The satisfying integer assignments provided by the theorem prover are then used to selectively increase domain sizes and generate fresh SAT-encodings of φ. The efficiency of this approach derives from the ability of SAT solvers to extract small unsatisfiable cores, leading to small abstracted formulas. We present experimental results which suggest that our algorithm is considerably more efficient than directly invoking the theorem prover on the original formula.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Daniel Kroening
    • 1
  • Joël Ouaknine
    • 1
  • Sanjit A. Seshia
    • 1
  • Ofer Strichman
    • 2
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityPittsburghUSA
  2. 2.Faculty of Industrial Engineering, the TechnionHaifaIsrael

Personalised recommendations