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Two-thirds simulation indexes and modal logic characterization

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Abstract

Two-thirds simulation provides a kind of abstract description of an implementation with respect to a specification. In order to characterize the approximate two-thirds simulation, we propose the definition of a two-thirds simulation index which expresses the degree to which a binary relation between processes is two-thirds simulation. λ-two-thirds simulation and its substitutivity laws are given in this paper. And, based on λ-two-thirds simulation, we present a measure model for describing the degree of approximation between processes. In particular, we give the modal logical characterization of λ-two-thirds simulation.

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References

  1. Hoare C A R. Communication Sequential Processes. Englewood Cliffs: Prentice Hall, 1985

    Google Scholar 

  2. Brookes S D, Hoare C A R, Roscoe A W. A theory of communicating sequential processes. Journal of the ACM, 1984, 31(3): 560–599

    Article  MATH  MathSciNet  Google Scholar 

  3. Olderog E R, Hoare C A R. Specification-oriented semantics for communicating processes. Acta Informatica, 1986, 23(1): 9–66

    Article  MATH  MathSciNet  Google Scholar 

  4. Park D. Concurrency and automata on infinite sequences. In: Proceedings of 5th GI-Conference on Theoretical Computer Science. 1981, 167–183

  5. Bloom B, Istrail S, Meyer A R. Bisimulation can’t be traced. Journal of the ACM, 1995, 42(1): 232–268

    Article  MATH  MathSciNet  Google Scholar 

  6. Milner R. A calculus of communicating systems. Lecture Notes in Computer Science, 1980, 92: 260–278

    MathSciNet  Google Scholar 

  7. Larsen K G, Skou A. Bisimulation through probabilistic testing. Journal of Information and Computation, 1991, 94(1): 1–28

    Article  MATH  MathSciNet  Google Scholar 

  8. Glabbeek R J. The linear time-branching time spectrum i-the semantics of concrete, sequential processes. http://theory.stanford.edu/rvg

  9. He J F, Hoare T. Equating bisimulation with refinement. Technical report, UNU-IIST, Macau, 2003

    Google Scholar 

  10. Ying M S, Wirshing M. Approximate bisimilarity and its application. Technical report, Institutfur Informatik, Ludwig-Maximilians-Universitat Munchen, 1999

  11. Ying M S. Bisimulation indexes and their applications. Theoretical Computer Science, 2002, 275(1–2): 1–68

    Article  MATH  MathSciNet  Google Scholar 

  12. Ying M S. Topology in Process Calculus: Approximate Correctness and Infinite Evolution of Concurrency Programs. New York: Springer-Verlag, 2001

    MATH  Google Scholar 

  13. Milner R. A complete inference system for a class of regular behaviours. Journal of Computer and System Sciences, 1984, 28(3): 439–466

    Article  MATH  MathSciNet  Google Scholar 

  14. Hennessy M, Milner R. Algebraic laws for nondeterminism and concurrency. Journal of the ACM, 1985, 32(1): 137–161

    Article  MATH  MathSciNet  Google Scholar 

  15. Milner R. Communication and Concurrency. New York: Prentice Hall, 1989

    MATH  Google Scholar 

  16. Minler R. Communicating and Mobile Systems: the π-calculus. Cambridge: Cambridge University Press, 1999

    Google Scholar 

  17. Plotkin G D. A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, 1981

  18. Engelking R. General Topology. Warszawa: Polish Scientific Publisher, 1977

    MATH  Google Scholar 

  19. Giacalone A, Jou C C, Smolka S A. Algebraic reasoning for probabilistic concurrent systems. In: Proceeding of Working Conference on Programming Concepts and Methods. 1990, 443–458

  20. Giacalone A, Jou C C, Smolka S A. Probabilistic in processes: an algebraic/operational framework. Technical report, Department of Computer Science, SUNY at Stony Brook, 1988

  21. Song L, Deng Y X, Cai X. Towards automatic measurement of probabilistic processes. In: Proceedings of the 7th International Conference on Quality Software. 2007, 50–59

  22. Deng Y X, Chothia T, Palamidessi C, Pang J. Metrics for actionlabelled quantitative transition systems. In: Proceedings of the 3rd Workshop on Quantitative Aspects of Programming Languages. 2005, 79–96

  23. Alves de Medeiros A K, van der Aalst W M P, Wejiters A J M M. Quantifying process equivalence based on observed behavior. Data & Knowledge Engineering, 2008, 64(1): 55–74

    Article  Google Scholar 

  24. Zhang J J, Zhu Z H. A modal characterization of λ-bisimilarity. International Journal of Software Informatics, 2007, 1(1): 85–99

    Google Scholar 

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Authors and Affiliations

  1. School of Computer Science and Technology, Huaibei Normal University, Huaibei, 235000, China

    Yanfang Ma

  2. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    Min Zhang & Yixiang Chen

  3. School of Mathematical Sciences, Huaibei Normal University, Huaibei, 235000, China

    Liang Chen

Authors
  1. Yanfang Ma
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  2. Min Zhang
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  3. Yixiang Chen
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  4. Liang Chen
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Correspondence to Yanfang Ma.

Additional information

Yanfang Ma is a lecturer in the School of Computer Science and Technology at Huaibei Normal University. She received her PhD degree in technology of computer science from East China Normal University in June 2010. Her research interests are on formalization of software, semantics of programs and trustworthiness measure model of software, with a special focus on the correctness of software. Recently, she was appointed project leader of the Open Fund of Shanghai Key Laboratory of Trustworthy Computing and the Key Research Foundation of Higher Education of Anhui Province.

Min Zhang is an assistant professor in the School of Software Engineering at East China Normal University since 2007. She received her PhD degree jointly from Shanghai Jiao Tong University and University Paris VII in 2007. Her research interests include formal methods, trustworthiness computation, and process calculus, with a particular emphasis on bisimulation of hybrid automata. Recently, she was appointed the project leader of the Fundamental Research Funds for the Central Universities.

Yixiang Chen is a Professor of Computer Science and Technology at the Software Engineering Institute (SEI), East China Normal University (ECNU), where he is coordinating Trustworthy Software, Internet of Things and Cloud Computing related research activities. Professor Chen is Vice-Dean of SEI and vice-director of the Shanghai Key Lab for Trustworthy Computing. He directs the Engineering Research Center for Software/Hardware Codesign (Shone), MoE of China. Prof. Chen is member of the Cloud Computing Experts Association of the Chinese Institute of Electronics and Vice Chair of the Shanghai Pudong IoT Alliance.

Liang Chen received his MSc degree in computation mathematics from Shanghai University in 2008. Now He is pursuing his PhD in the department of mathematics of Shanghai University. His research interests include rational approximation, design and analysis of algorithms.

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Ma, Y., Zhang, M., Chen, Y. et al. Two-thirds simulation indexes and modal logic characterization. Front. Comput. Sci. China 5, 454–471 (2011). https://doi.org/10.1007/s11704-011-0140-9

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