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On the Discriminating Power of Testing Equivalences for Reactive Probabilistic Systems: Results and Open Problems
BibTeX
@MISC{Bernardo_onthe,
author = {Marco Bernardo and Davide Sangiorgi and Valeria Vignudelli},
title = {On the Discriminating Power of Testing Equivalences for Reactive Probabilistic Systems: Results and Open Problems},
year = {}
}
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Abstract
Abstract. Testing equivalences have been deeply investigated on fully nondeterministic processes, as well as on processes featuring probabil-ities and internal nondeterminism. This is not the case with reactive probabilistic processes, for which it is only known that the discrimi-nating power of probabilistic bisimilarity is achieved when admitting a copying capability within tests. In this paper, we introduce for reactive probabilistic processes three testing equivalences without copying, which are respectively based on reactive probabilistic tests, fully nondetermin-istic tests, and nondeterministic and probabilistic tests. We show that the three testing equivalences are strictly finer than probabilistic failure-trace equivalence, and that the one based on nondeterministic and prob-abilistic tests is strictly finer than the other two, which are incomparable with each other. Moreover, we provide a number of facts that lead us to conjecture that (i) may testing and must testing coincide on reactive probabilistic processes and (ii) nondeterministic and probabilistic tests reach the same discriminating power as probabilistic bisimilarity. 1
Keyphrases
testing equivalence open problem reactive probabilistic system reactive probabilistic process discriminating power probabilistic test probabilistic bisimilarity copying capability nondeterministic process nondetermin-istic test prob-abilistic test internal nondeterminism probabilistic failure-trace equivalence discrimi-nating power reactive probabilistic test
