Applications of Craig Interpolation to Model Checking
A Craig interpolant  for a mutually inconsistent pair of formulas (A,B) is a formula that is (1) implied by A, (2) inconsistent with B, and (3) expressed over the common variables of A and B. It is known that a Craig interpolant can be efficiently derived from a refutation of A ∧ B, for certain theories and proof systems. For example, interpolants can be derived from resolution proofs in propositional logic, and for systems of linear inequalities over the reals [6,4]. These methods have been recently extended to combine linear inequalities with uninterpreted function symbols, and to deal with integer models . One key aspect of these procedures is that the yield quantifier-free interpolants when the premises A and B are quantifier-free.
- 2.Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from proofs. In: ACM Symp. on Principles of Prog. Lang, POPL 2004 (2004) (to appear)Google Scholar
- 7.Saïdi, H., Graf, S.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)Google Scholar