Removing redundant refusals: minimal complete test suites for failure trace semantics

We explore the problem of finding a minimal complete test suite for refusal trace (or failure trace) semantics. Our approach is based on generating a minimal complete set of forbidden refusal traces and utilises several interesting insights into the semantics. In particular, we identify a key class of refusals called fundamental refusals which essentially determine the refusal trace semantics, and the associated equivalence relation. We then propose a small but not necessarily minimal test suite, which can be constructed with a simple algorithm. Subsequently, we provide an enumerative method to remove all redundant traces from our complete test suite, which comes in two variants, depending on whether we wish to retain the highly desirable uniform completeness.

We also address a related problem from modal logic, namely the construction of a characteristic formula of a given process with respect to refusal trace semantics, using a variant of Hennessy-Milner logic with recursion.