Computer Science Department
School of Computer Science, Carnegie Mellon University


Abstraction-based Satisfiability Solving
of Presbuerger Arithmetic

Daniel Kroening, Joël Ouaknine, Sanjit Seshia, Ofer Strichman

January 2004

Keywords: Presburger arithmetic, Boolean satisfiability, theorem proving, abstraction

We present a new abstraction-based framework for deciding satisfuability of quantifier-free Presburger arithmetic formulas. Given a Presburger formula ø, our algorithm invokes a SAT solver to produce proofs of unsatisfiability of approximations of ø. These proofs are in turn used to generate abstractions of ø as inputs to a theorem prover. The SAT-encodings of the approximations of ø 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 ø. 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.

16 pages

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