Generating Longest Counterexample: On the Cross-roads of Mixed Integer Linear Programming and SMT

We present a technique for obtaining the longest counterexample - the execution that stays in the unsafe set for the longest (not necessarily contiguous) time, for a safety specification of linear hybrid systems. Given that hybrid systems are infinite state systems, the number of counterexamples for safety violations are potentially infinite. Therefore, searching for the right counterexample is very challenging. We employ two frameworks for solving this problem: first is an Mixed Integer Linear Program (MILP) formulation and second is to encode counterexamples using Satisfiability Module Theory (SMT) solvers. We evaluate these frameworks on several linear hybrid systems with up to 30 dimensions.