Property-directed reachability as abstract interpretation in the monotone theory

Inferring inductive invariants is one of the main challenges formal verification. The theory abstract interpretation provides a rich framework to devise invariant inference algorithms. One latest breakthroughs in property-directed reachability (PDR), but research community views PDR and as mostly unrelated techniques. This paper shows that, surprisingly, propositional can be formulated an algorithm logical domain. More precisely, we define version PDR, called Λ-PDR, which all generalizations counterexamples are used strengthen frame. In this way, there no need refine frames after their creation, because possible supporting facts included advance. We analyze using notions from Bshouty’s monotone theory, originally developed context exact learning. show that inherent overapproximation between algorithm’s related theory. then new domain best transformer performs overapproximation, it captures process, i.e., Λ-PDR corresponds Kleene iterations with provide some sufficient conditions for when process converges small number iterations, sometimes exponential gap required naive forward reachability. These results firm theoretical foundation benefits how tackles