Skip to main content
SpringerLink
Log in

Approximate reachability and bisimulation equivalences for transition systems

  • Published:
Transactions of Tianjin University Aims and scope Submit manuscript

Abstract

Using Baire metric, this paper proposes a generalized framework of transition system approximation by developing the notions of approximate reachability and approximate bisimulation equivalences. The proposed framework captures the traditional exact equivalence as a special case. Approximate reachability equivalence is coarser than approximate bisimulation equivalence, just like the hierarchy of the exact ones. Both approximate equivalences satisfy the transitive property, consequently, they can be used in transition system approximation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. van Glabbeek R J. The linear time-branching time spectrum i-The semantics of concrete, sequential processes. In: Handbook of Process Algebra[M]. Elsevier Science, Amsterdam, the Netherlands, 2001.

    Google Scholar 

  2. Fuhrmann P A, Helmke U. Reachability, observability and strict equivalence of networks of linear systems[J]. Mathematics of Control, Signals, and Systems, 2013, 25(4): 437–471.

    Article  MathSciNet  MATH  Google Scholar 

  3. Churchill M, Mosses P D. Modular bisimulation theory for computations and values. In: Foundations of Software Science and Computation Structures[M]. Springer Berlin Heidelberg, Germany, 2013.

    Google Scholar 

  4. Ciric M, Ignjatovic J, Basic M et al. Nondeterministic automata: Equivalence, bisimulations, and uniform relations[J]. Information Sciences, 2014, 261: 185–218.

    Article  MathSciNet  Google Scholar 

  5. van Breugel F. An introduction to metric semantics: Operational and denotational models for programming and specification languages[J]. Theoretical Computer Science, 2001, 258(1/2): 1–98.

    Article  MathSciNet  MATH  Google Scholar 

  6. Klin B, Sassone V. Structural operational semantics for stochastic and weighted transition systems[J]. Information and Computation, 2013, 227: 58–83.

    Article  MathSciNet  MATH  Google Scholar 

  7. Girard A, Pappas G J. Approximation metrics for discrete and continuous systems[J]. IEEE Transactions on Automatic Control, 2007, 52(5): 782–798.

    Article  MathSciNet  Google Scholar 

  8. Baire R. The representation of discontinuous function[J]. Acta Mathematica, 1906, 30(1): 1–48(in French).

    Article  MathSciNet  Google Scholar 

  9. Cao Y Z, Ying M. Similarity-based supervisory control of discrete-event systems[J]. IEEE Transactions on Automatic Control, 2006, 51(2): 325–330.

    Article  MathSciNet  Google Scholar 

  10. Cao Y Z, Chen G Q. Towards approximate equivalences of workflow processes[C]. In: Proceedings of the 1st International Conference on E-Business Intelligence (ICEBI2010). Kunming, China, 2010.

    Google Scholar 

  11. Yang H, Jiang B, Cocquempot V. Fault tolerant control and hybrid systems. In: Fault Tolerant Control Design for Hybrid Systems[M]. Springer-Verlag Berlin Heidelberg, Germany, 2010.

    Chapter  Google Scholar 

  12. Girard A, Julius A A, Pappas G J. Approximate simulation relations for hybrid systems[J]. Discrete Event Dynamic Systems, 2008, 18(2): 163–179.

    Article  MathSciNet  MATH  Google Scholar 

  13. Girard A, Pappas G J. Approximate bisimulation: A bridge between computer science and control theory[J]. European Journal of Control, 2011, 17(5/6): 568–578.

    Article  MathSciNet  MATH  Google Scholar 

  14. Julius A A, D’Innocenzo A, Di Benedetto M D et al. Approximate equivalence and synchronization of metric transition systems[J]. Systems & Control Letters, 2009, 58(2): 94–101.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer and Information Technology, Beijing Jiaotong University, Beijing, 100044, China

    Chao Wang  (王 超) & Jun Fu  (付 军)

  2. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, 530006, China

    Jinzhao Wu  (吴尽昭)

  3. Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China

    Hongyan Tan  (谭红艳)

Authors
  1. Chao Wang  (王 超)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinzhao Wu  (吴尽昭)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongyan Tan  (谭红艳)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jun Fu  (付 军)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinzhao Wu  (吴尽昭).

Additional information

Supported by the National Natural Science Foundation of China(No. 11371003 and No. 11461006), the Natural Science Foundation of Guangxi(No. 2011GXNSFA018154 and No. 2012GXNSFGA060003).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C., Wu, J., Tan, H. et al. Approximate reachability and bisimulation equivalences for transition systems. Trans. Tianjin Univ. 22, 19–23 (2016). https://doi.org/10.1007/s12209-016-2565-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12209-016-2565-6

Keywords

Search

Navigation