Testing from Partial Finite State Machines without Harmonised Traces

This paper concerns the problem of testing from a partial, possibly non-deterministic, finite state machine (FSM) S. Two notions of correctness (quasi-reduction and quasi-equivalence) have previously been defined for partial FSMs but these, and the corresponding test generation techniques, only apply to FSMs that have harmonised traces. We show how quasi-reduction and quasi-equivalence can be generalised to all partial FSMs. We also consider the problem of generating an m-complete test suite from a partial FSM S: a test suite that is guaranteed to determine correctness as long as the system under test has no more than m states. We prove that we can complete S to form a completely-specified non-deterministic FSM S' such that any m-complete test suite generated from S' can be converted into an m-complete test suite for S. We also show that there is a correspondence between test suites that are reduced for S and S' and also that are minimal for S and S'.