Bounded model checking and induction: From refutation to verification

We explore the combination of bounded model checking and induction for proving safety properties of infinite-state systems. In particular, we define a general k-induction scheme and prove completeness thereof A main characteristic of our methodology is that strengthened invariants are generated from failed k-induction proofs. This strengthening step requires quantifier-elimination, And we propose a lazy quantifier-elimination procedure, which delays expensive computations of disjunctive normal forms when possible. The effectiveness of induction based on bounded model checking and invariant strengthening is demonstrated using infinite-state systems ranging from communication protocols to timed automata and (linear) hybrid automata.