Property Directed Equivalence via Abstract Simulation

We present a novel approach for automated incremental verification that employs both reusable and relational specifications of software to incrementally verify pairs of programs with possibly nested loops. It analyzes two programs, P the one already verified, and Q the one needed to be verified, and proceeds by detecting an abstraction αP of P and a simulation ρ, such that αP simulates Q via ρ. The key idea behind our simulation synthesis is to drive construction of both αP and ρ by the safe inductive invariants of P , thus guaranteeing the property preservations by the results. Finally, our approach allows effective lifting of the safe inductive invariants of P to Q using only αP and ρ. Based on our evaluation, in many cases when the absolute equivalence between programs cannot be proven, our approach is able to establish the property directed equivalence, confirming that the program Q is safe.