A Testing Theory for Generally Distributed Stochastic Processes

In this paper we present a testing theory for stochastic processes. This theory is developed to deal with processes which probability distributions are not restricted to be exponential. In order to define this testing semantics, we compute the probability with which a process passes a test before an amount of time has elapsed. Two processes will be equivalent if they return the same probabilities for any test T and any time t. The key idea consists in joining all the random variables associated with the computations that the composition of process and test may perform. The combination of the values that this random variable takes and the probabilities of executing the actions belonging to the computation will give us the desired probabilities. Finally, we relate our stochastic testing semantics with other notions of testing.

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