Integration of Quantifier Eliminator with Model Checker and Compositional Reasoner

We present our work on integration of quantifier elimination (QE) technique with model checking and compositional verification. We begin by showing how quantifier elimination problems arise in these applications. In a k-induction based model checking approach, the verification problems of the base and inductive steps can be reduced to the QE problems in which all the variables are existentially quantified. It follows that a k-induction based model checker can be extended with QE tools to provide back-end solver options. Our implementation of integrating the QE tool Redlog with the model-checker JKind showed the successful resolution of a non-linear computation (emanating from a fuzzy logic operation) that the SMT-solver supported JKind was unable to resolve. Thus the QE tool provides a parallel option to the model-checker. The integrations of the QE tool Redlog with the model-checker JKind has been completed by us, and relies on writing the SMT-to-Redlog translator. On the other hand, in compositional verification, the goal is to prove a system level assume-guarantee style contract from the given component level contracts. The existing compositional verification tool AGREE tries to sequentially prove that each component's assumption is satisfied by the system assumption and other components' guarantees, following which the conjunction of all component contracts and system assumption is used to verify the system guarantee. In contrast, we propose a QE-based approach to derive, in a single step, the strongest system contract, from which any postulated system contract can be verified by performing a simple implication verification from the former to the later. We show how the compositional reasoner AGREE can be strengthened through its integration with the QE tool Redlog. We implemented our above approaches in a new prototype tool called ReLIC (Reduced Logic Inference for Composition) and demonstrated it through an illustrative example.