Efficient Computation of Recurrence Diameters

SAT based Bounded Model Checking (BMC) is an efficient method for detecting logical errors in finite-state transition systems. Given a transition system, an LTL property, and a user defined bound k, a bounded model checker generates a propositional formula that is satisfiable if and only if a counterexample to the property of length up to k exists. Standard SAT checkers can be used to check this formula. BMC is complete ifk is larger than some pre-computed threshold. It is still unknown how to compute this threshold for general properties. We show that the longest initialized loop-free path in the state graph, also known as the recurrence diameter, is sufficient for Fp properties. The recurrence diameter is also a known over-approximation for the threshold of simple safety properties (Gp). We discuss various techniques to compute the recurrence diameter efficiently and provide experimental results that demonstrate the benefits of using the new approach.