An interpolating theorem prover

We present a method of deriving Craig interpolants from proofs in the quantifier-free theory of linear inequality and uninterpreted function symbols, and an interpolating theorem prover based on this method. The prover has been used for predicate refinement in the BLAST software model checker, and can also be used directly for model checking infinite-state systems, using interpolation-based image approximation.

[1]  Hassen Saïdi,et al.  Construction of Abstract State Graphs with PVS , 1997, CAV.

[2]  Harald Ruess,et al.  Lazy Theorem Proving for Bounded Model Checking over Infinite Domains , 2002, CADE.

[3]  Karem A. Sakallah,et al.  GRASP—a new search algorithm for satisfiability , 1996, ICCAD 1996.

[4]  Shuvendu K. Lahiri,et al.  A Symbolic Approach to Predicate Abstraction , 2003, CAV.

[5]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[6]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[7]  William Craig,et al.  Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory , 1957, Journal of Symbolic Logic.

[8]  Greg Nelson,et al.  Simplification by Cooperating Decision Procedures , 1979, TOPL.

[9]  Pavel Pudlák,et al.  Lower bounds for resolution and cutting plane proofs and monotone computations , 1997, Journal of Symbolic Logic.

[10]  Kenneth L. McMillan,et al.  Interpolation and SAT-Based Model Checking , 2003, CAV.

[11]  Kenneth L. McMillan,et al.  Automatic Abstraction without Counterexamples , 2003, TACAS.

[12]  David A. Plaisted,et al.  A Structure-Preserving Clause Form Translation , 1986, J. Symb. Comput..

[13]  William Craig,et al.  Linear reasoning. A new form of the Herbrand-Gentzen theorem , 1957, Journal of Symbolic Logic.

[14]  Jan Krajícek,et al.  Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic , 1997, Journal of Symbolic Logic.