A testing scenario for probabilistic processes

• Published in: Journal of the ACM Vol. 54; no. 6; p. 29
• Main Authors: Cheung, Ling, Stoelinga, Mariëlle, Vaandrager, Frits
• Format: Journal Article
• Language: English
• Published: New York, NY Association for Computing Machinery 01.12.2007
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Approximation; Closures; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Equivalence; Exact sciences and technology; Hypothesis testing; Machinery; Mathematical analysis; Metric space; Probabilistic methods; Probability; Probability theory; Software; Studies; Theoretical computing; Process algebra; CPO; Probabilistic approach; Metric space; Closure; Theory; testing; trace distributions; button- pushing scenario; Finite automaton; Verification; metric spaces; Modeling; Concurrency theory; Hypothesis test; Statistical test; probabilistic automata; Probabilistic automaton; Concurrency; approximation induction principle; observational equivalence
• ISSN: 0004-5411; 1557-735X
• DOI: 10.1145/1314690.1314693

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.