Computer Aided Verification

Volume 3114 of the series Lecture Notes in Computer Science pp 308-320

Abstraction-Based Satisfiability Solving of Presburger Arithmetic

  • Daniel KroeningAffiliated withComputer Science Department, Carnegie Mellon University
  • , Joël OuaknineAffiliated withComputer Science Department, Carnegie Mellon University
  • , Sanjit A. SeshiaAffiliated withComputer Science Department, Carnegie Mellon University
  • , Ofer StrichmanAffiliated withFaculty of Industrial Engineering, the Technion

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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.