Testing and Refinement for Nondeterministic and Probabilistic Processes

Transition systems are a basic semantic model for formal description, specification, and analysis of concurrent and distributed systems. In order to describe and analyze aspects of reliability, such as the likelihood of trace and failure, this model has been extended in various ways to handle probabilistic behavior. To use these models for specification and stepwise development of systems, it is important to develop appropriate refinement preorders. In the paper, we develop refinement preorders based on a framework of testing for a model that represents both nondeterministic and probabilistic choices as independent concepts [YL92]. Our main contribution is a notion of reward testing, and a denotational characterization of a testing preorder, which corresponds to a natural probabilistic extension of the trace model [Hoa85].

[1]  Moshe Y. Vardi.  Automatic verification of probabilistic concurrent finite state programs , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[2]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[3]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

[4]  Scott A. Smolka,et al.  Algebraic Reasoning for Probabilistic Concurrent Systems , 1990, Programming Concepts and Methods.

[5]  Bengt Jonsson,et al.  A framework for reasoning about time and reliability , 1989, [1989] Proceedings. Real-Time Systems Symposium.

[6]  Wang Yi,et al.  Testing Probabilistic and Nondeterministic Processes , 1992, PSTV.

[7]  Mihalis Yannakakis,et al.  The complexity of probabilistic verification , 1995, JACM.

[8]  Rocco De Nicola,et al.  Testing Equivalences for Processes , 1984, Theor. Comput. Sci..

[9]  Kim Guldstrand Larsen,et al.  Specification and refinement of probabilistic processes , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[10]  S. Purushothaman Iyer,et al.  Reasoning About Probabilistic Behavior in Concurrent Systems , 1987, IEEE Transactions on Software Engineering.

[11]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

[12]  Gavin Lowe,et al.  Probabilities and priorities in timed CSP , 1993 .

[13]  Micha Sharir,et al.  Probabilistic temporal logics for finite and bounded models , 1984, STOC '84.

[14]  Bernhard Steffen,et al.  Reactive, generative, and stratified models of probabilistic processes , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[15]  Zohar Manna,et al.  The anchored version of the temporal framework , 1988, REX Workshop.

[16]  Michael K. Molloy.  Performance Analysis Using Stochastic Petri Nets , 1982, IEEE Transactions on Computers.

[17]  Dexter Kozen,et al.  A probabilistic PDL , 1983, J. Comput. Syst. Sci..

[18]  Rance Cleaveland,et al.  Testing Preorders for Probabilistic Processes , 1992, ICALP.

[19]  C. A. R. Hoare,et al.  Communicating Sequential Processes (Reprint) , 1983, Commun. ACM.

[20]  Bengt Jonsson,et al.  A calculus for communicating systems with time and probabilities , 1990, [1990] Proceedings 11th Real-Time Systems Symposium.