Testing from Partial Finite State Machines without Harmonised Traces

Abstract

This paper concerns the problem of testing from a partial, possibly non-deterministic, finite state machine (FSM) ${\mathcal S}$ . 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 ${\mathcal S}$ : 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 ${\mathcal S}$ to form a completely-specified non-deterministic FSM ${\mathcal S}^{\prime}$ such that any $m$ -complete test suite generated from ${\mathcal S}^{\prime}$ can be converted into an $m$ -complete test suite for ${\mathcal S}$ . We also show that there is a correspondence between test suites that are reduced for ${\mathcal S}$ and ${\mathcal S}^{\prime}$ and also that are minimal for ${\mathcal S}$ and ${\mathcal S}^{\prime}$ .