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In the theory of testing for Markovian processes developed so far,exponentially timed internal actions are not admitted within processes. Whenpresent, these actions cannot be abstracted away, because their execution takesa nonzero amount of time and hence can be observed. On the other hand, theymust be carefully taken into account, in order not to equate processes that aredistinguishable from a timing viewpoint. In this paper, we recast thedefinition of Markovian testing equivalence in the framework of a Markovianprocess calculus including exponentially timed internal actions. Then, we showthat the resulting behavioral equivalence is a congruence, has a sound andcomplete axiomatization, has a modal logic characterization, and can be decidedin polynomial time.

Markovian Testing Equivalence and Exponentially Timed Internal Actions