Widening Arithmetic Automata

Model checking of infinite state systems is undecidable, therefore, there are instances for which fixpoint computations used in infinite state model checkers do not converge. Given a widening operator one can compute an upper approximation of a least fixpoint in finite number of steps even if the least fixpoint is uncomputable. We present a widening operator for automata encoding integer sets. We show how widening can be used to verify safety properties that cannot be verified otherwise. We also show that the dual of the widening operator can be used to detect counter examples for liveness properties. Finally, we show experimentally how the same technique can be used to verify properties of complex infinite state systems efficiently.