Testing Nondeterministic Finite State Machines with Respect to the Separability Relation

In this paper, we propose a fault model and a method for deriving complete test suites for nondeterministic FSMs with respect to the separability relation. Two FSMs are separable if there exists an input sequence such that the sets of output responses of these FSMs to the sequence do not intersect. In contrast to the well-known reduction and equivalence relations, the separability relation can be checked when the «all weather conditions» assumption does not hold for a nondeterministic Implementation Under Test (IUT). A (complete) test suite derived from the given (nondeterministic) FSM specification using the separability relation can detect every IUT that is separable from the given specification after applying each test case only once. Two algorithms are proposed for complete test derivation without the explicit enumeration of all possible implementations. The first algorithm can be applied when the set of possible implementations is the set of all complete nondeterministic submachines of a given mutation machine. The second algorithm is applied when the upper bound on the number of states of an IUT is known.