Skip to main content
SpringerLink
Log in

A polynomial time algorithm for checking regularity of totally normed process algebra

  • Published:
Journal of Shanghai Jiaotong University (Science) Aims and scope Submit manuscript

Abstract

A polynomial algorithm for the regularity problem of weak and branching bisimilarity on totally normed process algebra (PA) processes is given. Its time complexity is \(\mathcal{O}(n^3 + mn)\), where n is the number of transition rules and m is the maximal length of the rules. The algorithm works for totally normed basic process algebra (BPA) as well as basic parallel process (BPP).

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. Hopcroft J, Motwani R, Ullman J. Introduction to automata theory, languages and computation [M]. Boston: Addison-Wesley Publishing Company, 1979.

    Google Scholar 

  2. Park D. Concurrency and automata on infinite sequences [J]. Theoretical Computer Science, 1981, 104: 167–183.

    Article  Google Scholar 

  3. Milner R. Comunication and concurrency [M]. Upper Saddle River, NJ, USA: Prentice Hall, 1989.

    Google Scholar 

  4. Baeten J C M, Bergstra J A, Klop J W. Decidability of bisimulation equivalence for process generating context-free languages [J]. Journal of the Association for Computing Machinery, 1993, 40(3): 653–682.

    Article  MATH  MathSciNet  Google Scholar 

  5. Christensen S, Hüttel H, Stirling C. Bisimulation equivalence is decidable for all context-free processes [J]. Lecture Notes in Computer Science, 1992, 630: 138–147.

    Article  Google Scholar 

  6. Burkart O, Caucal D, Moller F, et al. Verifcation on infinite structures: Handbook of process algebra [M]. Cambridge: Cambridge University Press, 2001: 545–623.

    Book  Google Scholar 

  7. Moller F, Smolka S, Srba J. On the computational complexity of bisimulation, redux [J]. Information and Computation, 2004, 194(2): 129–143.

    Article  MATH  MathSciNet  Google Scholar 

  8. Kučera A, Jančar P. Equivalence-checking on infinite-state systems: Techniques and results [J]. Theory and Practice of Logic Programming, 2006, 6(3): 227–264.

    Article  MATH  MathSciNet  Google Scholar 

  9. Srba J. Roadmap of infinite results [J]. Bullitin in EATCS, 2002 (78): 163–175.

    MATH  MathSciNet  Google Scholar 

  10. Mayr R. Process rewrite systems [J]. Information and Computation, 2000, 156(1): 264–286.

    Article  MATH  MathSciNet  Google Scholar 

  11. Burkart O, Caucal D, Steffen B. An elementary bisimulation decision procedure for arbitrary contextfree processes [J]. Mathematical Foundations of Computer Science, 1995, 969: 423–433.

    MathSciNet  Google Scholar 

  12. Hirshfeld Y, Jerrum M, Moller F. A polynomial algorithm for deciding bisimilarity of normed contextfree processes [J]. Journal of Theoretical Computer Science, 1996, 158(1): 143–159.

    Article  MATH  MathSciNet  Google Scholar 

  13. Kučera A. Regularity is decidable for normed PA processes in polynomial time [C]//Foundations of Software Technology and Theoretical Computer Science. Geneva: Springer-Verlag, 1996: 111–122.

    Google Scholar 

  14. Jančar P. Strong bisimilarity on basic parallel processes in PSPACE-complete [C]//Proceedings of 18th Annual IEEE Symposium on Logic in Computer Science. Edinburgh: IEEE, 2003: 218–227.

    Google Scholar 

  15. Kot M. Regularity of BPP is PSPACE-complete [C]//Proceedings of the 3rd Ph. D. Workshop of Faculty of Electrical Engineering and Computer Science (WOFEX’05). Ostrava: WVSB-Technical University of Ostravay, 2005: 393–398.

    Google Scholar 

  16. Hirshfeld Y, Jerrum M, Moller F. A polynomial time algorithm for deciding bisimulation equivalence of normed basic parallel processes [J]. Mathematical Structures in Computer Science, 1996, 6(3): 251–259.

    Article  MATH  MathSciNet  Google Scholar 

  17. Hirshfeld Y, Jerrum M. Bisimulation equivalence is decidable for normed process algebra [J]. Automata, Languages and Programming, 1999, 1644: 412–421.

    MathSciNet  Google Scholar 

  18. Czerwiński W, Hofman P, Lasota S. Decidability of branching bisimulation on normed commutative context-free processes [J]. Lecture Notes in Computer Science, 2011, 6901: 528–542.

    Article  Google Scholar 

  19. Fu Y. Checking equality and regularity for normed BPA with silent moves [J]. Automata, Languages, and Programming, 2013, 7966: 238–249.

    Google Scholar 

  20. Hüttel H. Silence is golden: Branching bisimilarity is decidable for context-free processes [J]. Lecture Notes in Computer Science, 1992, 575: 2–12.

    Article  Google Scholar 

  21. Chen H. Decidability of weak bisimilarity for a subset of BPA [J]. Electronic Notes in Theoretical Computer Science, 2008, 212: 241–255.

    Article  Google Scholar 

  22. Chen H. More on weak bisimilarity of normed basic parallel processes [J]. Theory and Applications of Models of Computation, 2008, 4978: 192–203.

    Article  Google Scholar 

  23. van Glabbeek R, Weijland W. Branching time and abstraction in bisimulation semantics [J]. Journal of the Association for Computing Machinery, 1996, 43(3): 555–600.

    Article  MATH  Google Scholar 

  24. Srba J. Strong bisimilarity and regularity of basic parallel processes is PSPACE-hard [J]. Lecture Notes in Computer Science, 2002, 2285: 535–546.

    Article  MathSciNet  Google Scholar 

  25. Mayr R. Weak bisimilarity and regularity of BPA is EXPTIME-hard [C]//Proccedings of the 10th International Workshop on Expressiveness in Concurrency (EXPRESS’03). Marseilles, France: Elsevier Science Publishers, 2003: 160–143.

    Google Scholar 

  26. Srba J. Complexity of weak bisimilarity and regularity for BPA and BPP [J]. Electronic Notes in Theoretical Computer Science, 2003, 39(1): 79–93.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Basic Studies in Computing Science, Department of Computer Science and Engineering, Shanghai Jiaotong University, Shanghai, 200240, China

    Fei Yang  (杨 非) & Hao Huang  (黄 浩)

Authors
  1. Fei Yang  (杨 非)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao Huang  (黄 浩)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fei Yang  (杨 非).

Additional information

Foundation item: the National Natural Science Foundation of China (Nos. 61261130589 and 61033002) and the Fund of the Science and Technology Commission of Shanghai Municipality (No. 11XD1402800)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, F., Huang, H. A polynomial time algorithm for checking regularity of totally normed process algebra. J. Shanghai Jiaotong Univ. (Sci.) 20, 273–280 (2015). https://doi.org/10.1007/s12204-014-1555-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12204-014-1555-x

Key words

CLC number

Search

Navigation