A Testing Scenario for Probabilistic AutomataM.I.A. Stoelinga and F.W. Vaandrager. A Testing Scenario for Probabilistic Automata.
AbstractWe present a simple and intuitive testing scenario for image finite probabilistic automata. We introduce a notion of finite testing via a variant of the well-known machine. Under this scenario, two automata are deemed observationally equivalent if they cannot be distinguished by any finite test. We then 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 executions of an arbitrary probabilistic automaton A and generalize the Approximation Induction Principle by defining an algebraic CPO structure on the set of trace distributions of A. We also prove limit and convex closure properties of trace distributions in an appropriate metric space.