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A survey of modal logics characterising behavioural equivalences for non-deterministic and stochastic systems

Published online by Cambridge University Press:  01 February 2008

MARCO BERNARDO  and
STEFANIA BOTTA
MARCO BERNARDO
Affiliation:
Università di Urbino ‘Carlo Bo’, Istituto di Scienze e Tecnologie dell'Informazione, Italy
STEFANIA BOTTA
Affiliation:
Università di Urbino ‘Carlo Bo’, Istituto di Scienze e Tecnologie dell'Informazione, Italy
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Abstract

Behavioural equivalences are a means of establishing whether computing systems possess the same properties. The specific set of properties that are preserved by a specific behavioural equivalence clearly depends on how the system behaviour is observed and can usually be characterised by means of a modal logic. In this paper we consider three different approaches to the definition of behavioural equivalences – bisimulation, testing and trace – applied to three different classes of systems – non-deterministic, probabilistic and Markovian – and we survey the nine resulting modal logic characterisations, each of which stems from the Hennessy–Milner logic. We then compare the nine characterisations with respect to the logical operators, in order to emphasise the differences between the three approaches in the definition of behavioural equivalences and the regularities within each of them. In the probabilistic and Markovian cases we also address the issue of whether the probabilistic and temporal aspects should be treated in a local or global way and consequently whether the modal logic interpretation should be qualitative or quantitative.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Special Issue 1: in memory of Sauro Tulipani , February 2008 , pp. 29 - 55
Copyright
Copyright © Cambridge University Press2008

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References

Abramsky, S. (1987) Observational Equivalence as a Testing Equivalence. Theoretical Computer Science 53 225–241.CrossRefGoogle Scholar
Bernardo, M. (2007) Non-Bisimulation-Based Markovian Behavioral Equivalences. To appear in Journal of Logic and Algebraic Programming.CrossRefGoogle Scholar
Bernardo, M. and Botta, S. (2006) Modal Logic Characterization of Markovian Testing and Trace Equivalences. In: Proc. of the First Int. Workshop on Logic, Models and Computer Science (LMCS 2006), Camerino (Italy). Electronic Notes in Theoretical Computer Science.CrossRefGoogle Scholar
Bernardo, M. and Bravetti, M. (2003) Performance Measure Sensitive Congruences for Markovian Process Algebras. Theoretical Computer Science 290 117–160.CrossRefGoogle Scholar
Bernardo, M. and Cleaveland, R. (2000) A Theory of Testing for Markovian Processes. In: Proc. of the 11th Int. Conf. on Concurrency Theory (CONCUR 2000), State College (PA). Springer-Verlag Lecture Notes in Computer Science 1877 305–319.CrossRefGoogle Scholar
Bravetti, M. and Aldini, A. (2003) Discrete Time Generative-Reactive Probabilistic Processes with Different Advancing Speeds Theoretical Computer Science 290 355–406.CrossRefGoogle Scholar
Christoff, I. (1990) Testing Equivalences and Fully Abstract Models for Probabilistic Processes. In: Proc. of the First Int. Conf. on Concurrency Theory (CONCUR 1990), Amsterdam. Springer-Verlag Lecture Notes in Computer Science 458 126–140.CrossRefGoogle Scholar
Clark, G., Gilmore, S. and Hillston, J. (1999) Specifying Performance Measures for PEPA. In: Proc. of the 5th AMAST Int. Workshop on Formal Methods for Real Time and Probabilistic Systems (ARTS 1999), Bamberg (Germany). Springer-Verlag Lecture Notes in Computer Science 1601 211–227.CrossRefGoogle Scholar
Cleaveland, R., Dayar, Z., Smolka, S. A. and Yuen, S. (1999) Testing Preorders for Probabilistic Processes. Information and Computation 154 93–148.CrossRefGoogle Scholar
De Nicola, R., and Hennessy, M. (1983) Testing Equivalences for Processes. Theoretical Computer Science 34 83–133.CrossRefGoogle Scholar
van Glabbeek, R. J. (2001) The Linear Time – Branching Time Spectrum I. Handbook of Process Algebra, Elsevier 3–99.CrossRefGoogle Scholar
vanGlabbeek, R. J. Glabbeek, R. J., Smolka, S. A. and Steffen, B. (1995) Reactive, Generative and Stratified Models of Probabilistic Processes. Information and Computation 121 59–80.Google Scholar
Hennessy, (1985), M. Acceptance Trees. Journal of the ACM 32 896–928.CrossRefGoogle Scholar
Hennessy, M. and Milner, R. (1985) Algebraic Laws for Nondeterminism and Concurrency. Journal of the ACM 32 137–162.CrossRefGoogle Scholar
Hermanns, H. (2002) Interactive Markov Chains. Springer-Verlag Lecture Notes in Computer Science 2428.Google Scholar
Hillston, J. (1996) A Compositional Approach to Performance Modelling, Cambridge University Press.CrossRefGoogle Scholar
Hoare, C. A. R. (1985) Communicating Sequential Processes, Prentice Hall.Google Scholar
Jou, C.-C. and Smolka, S. A. (1990) Equivalences, Congruences and Complete Axiomatizations for Probabilistic Processes. In: Proc. of the First Int. Conf. on Concurrency Theory (CONCUR 1990), Amsterdam (The Netherlands). Springer-Verlag Lecture Notes in Computer Science 458 367–383.CrossRefGoogle Scholar
Kwiatkowska, M. Z. and Norman, G. J. (1998) A Testing Equivalence for Reactive Probabilistic Processes, Nice (France). In: Proc. of the 2nd Int. Workshop on Expressiveness in Concurrency (EXPRESS 1998). Electronic Notes in Theoretical Computer Science 16 (2)114–132.CrossRefGoogle Scholar
Larsen, K. G. and Skou, A. (1991) Bisimulation through Probabilistic Testing. Information and Computation 94 1–28.CrossRefGoogle Scholar
Milner, R. (1989) Communication and Concurrency, Prentice Hall.Google Scholar
Wolf, V., Baier, C. and Majster-Cederbaum, M. (2005) Trace Machines for Observing Continuous-Time Markov Chains. In: Proc. of the 3rd Int. Workshop on Quantitative Aspects of Programming Languages (QAPL 2005), Edinburgh (UK). Electronic Notes in Theoretical Computer Science 153 (2)259–277.CrossRefGoogle Scholar