Fair Testing through Probabilistic Testing

In this paper we deene a probabilistic testing semantics which can be used to alternatively characterize fair testing. The key idea is to deene a probabilistic semantics in such a way that two non-probabilistic processes are fair equivalent ii any probabilistic version of both processes are equivalent in our probabilistic testing semantics. In order to get this result we deene a simple probabilistic must semantics by saying that a probabilistic process must pass a test ii the probability with which the process passes the test equals 1. Finally, we present an algorithm for deciding whether the probability with which a nite-state process passes a nite-state test equals 1. Alternatively, this algorithm can be used for computing whether a nite-state process fairly passes a nite-state test. 1. INTRODUCTION Formal models of concurrency have been proved to be very useful to properly specify concurrent and distributed systems. In order to verify the properties held by these speciications some kind of semantics must be given to these syntactic processes. Several semantic models have been proposed in the literature, for example, failures model, bisimulations, testing semantics, axiomatic semantics, etc. In our opinion, among the previously cited semantic models, the closest to reality is testing. Testing semantics was deened and thoroughly studied in de Nicola and Hennessy, 1984, Hennessy, 1988], and this will be the approach considered here. In their model tests are just processes 1