Generalized counterexamples to liveness properties

We consider generalized counterexamples in the context of liveness property checking. A generalized counterexample comprises only a subset of values necessary to establish the existence of a concrete counterexample. While useful in various ways even for safety properties, the length of a generalized liveness counterexample may be exponentially shorter than that of a concrete counterexample, entailing significant potential algorithmic benefits. One application of this concept extends the k-LIVENESS proof technique of [1] to enable failure detection. The resulting algorithm is simple, and poses negligible overhead to k-LIVENESS in practice. We additionally propose dedicated algorithms to search for generalized liveness counterexamples, and to manipulate generalized counterexamples to and from concrete ones. Experiments confirm the capability of these techniques to detect failures more efficiently than existing techniques for various benchmarks.