Abstract
We present a process-algebraic language for Probabilistic I/O Automata (PIOA). To ensure that PIOA specifications given in our language satisfy the “input-enabled” property, which requires that all input actions be enabled in every state of a PIOA, we augment the language with a set of type inference rules. We also equip our language with a formal operational semantics defined by a set of transition rules. We present a number of results whose thrust is to establish that the typing and transition rules are sensible and interact properly. The central connection between types and transition systems is that if a term is well-typed, then in fact the associated transition system is input-enabled. We also consider two notions of equivalence for our language, weighted bisimulation equivalence and PIOA behavioral equivalence. We show that both equivalences are substitutive with respect to the operators of the language, and note that weighted bisimulation equivalence is a strict refinement of behavioral equivalence.
This research was supported in part by the National Science Foundation under Grant CCR-9988155 and the Army Research Office under Grants DAAD190110003 and DAAD190110019. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation, the Army Research Office, or other sponsors.
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References
Bernardo, M., Donatiello, L., Gorrieri, R.: A formal approach to the integration of performance aspects in the modeling and analysis of concurrent systems. Information and Computation 144(2), 83–154 (1998)
Brinksma, E., Hermanns, H.: Process algebra and Markov chains. In: Brinksma, E., Hermanns, H., Katoen, J.-P. (eds.) EEF School 2000 and FMPA 2000. LNCS, vol. 2090, pp. 183–231. Springer, Heidelberg (2001)
Buchholz, P.: Exact performance equivalence: An equivalence relation for stochastic automata. Theoretical Computer Science 215, 263–287 (1999)
Cleaveland, R., Parrow, J., Steffen, B.U.: The Concurrency Workbench: A semantics-based tool for the verification of concurrent systems. ACM TOPLAS 15(1) (1993)
De Nicola, R., Segala, R.: A process algebraic view of Input/Output Automata. Theoretical Computer Science 138(2) (1995)
Garland, S.J., Lynch, N.A.: Using I/O automata for developing distributed systems. In: Leavens, G.T., Sitaraman, M. (eds.) Foundations of Component-Based Systems, pp. 285–312. Cambridge University Press, Cambridge (2000)
Katoen, J.-P., Hermanns, H., Herzog, U.: Process algebra for performance evaluation. Theoretical Computer Science 274, 43–97 (2002)
Hillston, J.: The nature of synchronization. In: Herzog, U., Rettelbach, M. (eds.) Proceedings of the 2nd Workshop on Process Algebra and Performance Modeling, July 1994, pp. 51–70. University of Erlangen (1994)
Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)
Jonsson, B., Larsen, K.G., Yi, W.: Probabilistic extensions of process algebras. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra. Elsevier, Amsterdam (2001)
Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Information and Computation 94(1), 1–28 (1991)
Lynch, N.A., Tuttle, M.: Hierarchical correctness proofs for distributed algorithms. In: Proceedings of the 6th Annual ACM Symposium on Principles of Distributed Computing, pp. 137–151 (1987)
Plateau, B., Atif, K.: Stochastic automata networks for modeling parallel systems. IEEE Transactions on Software Engineering 17, 1093–1108 (1991)
Stark, E.W., Smolka, S.: Compositional analysis of expected delays in networks of probabilistic I/O automata. In: Proc. 13th Annual Symposium on Logic in Computer Science, Indianapolis, IN, June 1998, pp. 466–477. IEEE Computer Society Press, Los Alamitos (1998)
Stark, E.: On behavior equivalence for probabilistic I/O automata and its relationship to probabilistic bisimulation. Journal of Automata, Languages, and Combinatorics 8(2) (2003) (to appear)
Vaandrager, F.W.: On the relationship between process algebra and input/output automata. In: Sixth Annual Symposium on Logic in Computer Science (LICS 1991), Amsterdam, July 1991, pp. 387–398. Computer Society Press (1991)
Wu, S.-H., Smolka, S.A., Stark, E.W.: Compositionality and full abstraction for probabilistic I/O automata. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836. Springer, Heidelberg (1994)
Wu, S.-H., Smolka, S.A., Stark, E.W.: Composition and behaviors of probabilistic I/O automata. Theoretical Computer Science 176(1-2), 1–38 (1997)
Zhang, D., Cleaveland, R., Stark, E.W.: The integrated CWBNC/ PIOATool for functional and performance analysis of concurrent systems. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 431–436. Springer, Heidelberg (2003)
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Stark, E.W., Cleaveland, R., Smolka, S.A. (2003). A Process-Algebraic Language for Probabilistic I/O Automata. In: Amadio, R., Lugiez, D. (eds) CONCUR 2003 - Concurrency Theory. CONCUR 2003. Lecture Notes in Computer Science, vol 2761. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45187-7_13
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