A Testing Scenario for Probabilistic Processes

L. Cheung, M.I.A. Stoelinga and F.W. Vaandrager. A Testing Scenario for Probabilistic Processes. In Journal of the ACM 54(6), December 2007. Earlier version available as Technical Report ICIS-R06002, ICIS, Radboud University Nijmegen, January 2006. This is the full version of our ICALP'03 paper.Abstract

We introduce a notion of finite testing, based on statistical hypothesis tests, via a variant of the well-known trace machine. Under this scenario, two processes are deemed observationally equivalent if they cannot be distinguished by any finite test. We consider processes modeled as image finite probabilistic automata and prove that our notion of observational equivalence coincides with the trace distribution equivalence proposed by Segala. Along the way, we give an explicit characterization of the set of probabilistic generalize the Approximation Induction Principle by defining an also prove limit and convex closure properties of trace distributions in an appropriate metric space.