Abstract
We present a testing theory for Markovian processes in order to formalize a notion of efficiency which may be useful for the analysis of soft real time systems. Our Markovian testing theory is shown to enjoy close connections with the classical testing theory of De Nicola-Hennessy and the probabilistic testing theory of Cleaveland-Smolka et al. The Markovian testing equivalence is also shown to be coarser than the Markovian bisimulation equivalence. A fully abstract characterization is developed to ease the task of establishing testing related relationships between Markovian processes. It is then demonstrated that our Markovian testing equivalence, which is based on the (easier to work with) probability of executing a successful computation whose average duration is not greater than a given amount of time, coincides with the Markovian testing equivalence based on the (more intuitive) probability of reaching success within a given amount of time. Finally, it is shown that it is not possible to define a Markovian preorder which is consistent with reward based performance measures, thus justifying why a generic notion of efficiency has been considered.
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References
M. Bernardo, “Theory and Application of Extended Markovian Process Algebra”, Ph.D. Thesis, University of Bologna, 1999 (http://www.di.unito.it/~bernardo/)
M. Bernardo, W. R. Cleaveland, “A Theory of Efficiency for Markovian Processes”, Tech. Rep. UBLCS-99-02, University of Bologna, 1999
W. R. Cleaveland, M. C. B. Hennessy, “Testing Equivalence as a Bisimulation Equivalence”, in Formal Aspects of Computing 5:1–20, 1993
W. R. Cleaveland, S. A. Smolka, A. E. Zwarico, “Testing Preorders for Probabilistic Processes” in Proc. of ICALP’ 92, LNCS 623:708–719, 1992
R. De Nicola, M. C. B. Hennessy, “Testing Equivalences for Processes” in Theoretical Computer Science 34:83–133, 1983
H. Hermanns, “Interactive Markov Chains”, Ph.D. Thesis, University of Erlangen, 1998
H. Hermanns, M. Rettelbach, “Syntax, Semantics, Equivalences, and Axioms for MTIPP”, in Proc. of PAPM’ 94, pp. 71–87, Erlangen, 1994
J. Hillston, “A Compositional Approach to Performance Modelling” Cambridge University Press, 1996
J. Hillston, “Exploiting Structure in Solution: Decomposing Composed Models”, in Proc. of PAPM’ 98, pp. 1–15, 1998
R. A. Howard, “Dynamic Probabilistic Systems”, John Wiley & Sons, 1971
M. F. Neuts, “Matrix-Geometric Solutions in Stochastic Models-An Algorithmic Approach”, John Hopkins University Press, 1981
M. Nuñez, D. de Frutos, L. Llana, “Acceptance Trees for Probabilistic Processes”, in Proc. of CONCUR’ 95, LNCS 962:249–263, 1995
S. Yuen, W. R. Cleaveland, Z. Dayar, S. A. Smolka, “Fully Abstract Characterizations of Testing Preorders for Probabilistic Processes”, in Proc. of CONCUR’ 94, LNCS 836:497–512, 1994
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© 2000 Springer-Verlag Berlin Heidelberg
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Bernardo, M., Cleaveland, R. (2000). A Theory of Testing for Markovian Processes. In: Palamidessi, C. (eds) CONCUR 2000 — Concurrency Theory. CONCUR 2000. Lecture Notes in Computer Science, vol 1877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44618-4_23
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DOI: https://doi.org/10.1007/3-540-44618-4_23
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