Verification modulo theories

In this paper, we consider the problem of model checking fair transition systems expressed symbolically in the framework of Satisfiability Modulo Theories. This problem, referred to as Verification Modulo Theories, is tackled by combining two key elements from the legacy of Ed Clarke: SAT-based verification and abstraction refinement. We show how fundamental SAT-based algorithms have been lifted to deal with the extended expressiveness with a tight integration of abstraction within a CEGAR loop. In turn, the case of nonlinear theories is based on a CEGAR loop over the linear case. These two elements have also deeply impacted the development of the NuSMV model checker, born from a joint project between FBK and CMU, and its successor nuXmv, whose core integrates SMT-based techniques for VMT.