Skip to main content
SpringerLink
Log in

Hereditary History Preserving Bisimilarity Is Undecidable

  • Conference paper
  • First Online:
STACS 2000 (STACS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1770))

Included in the following conference series:

Abstract

History preserving bisimilarity (hp-bisimilarity) and hereditary history preserving bisimilarity (hhp-bisimilarity) are behavioural equivalences taking into account causal relationships between events of concurrent systems. Their prominent feature is being preserved under action refinement, an operation important for the top-down design of concurrent systems. We show that—unlike hp-bisimilarity—checking hhp-bisimilarity for finite labelled asynchronous transition systems is not decidable, by a reduction from the halting problem of 2-counter machines. To make the proof more transparent we introduce an intermediate problem of checking domino bisimilarity for origin constrained tiling systems, whose undecidability is interesting in its own right. We also argue that the undecidability of hhp-bisimilarity holds for finite labelled 1-safe Petri nets.

Basic Research in Computer Science, Centre of the Danish National Research Foundation.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Marek A. Bednarczyk. Hereditary history preserving bisimulations or what is the power of the future perfect in program logics. Technical report, Polish Academy of Sciences, Gdańsk, April 1991. Available at http://www.ipipan.gda.pl/~marek.

    Google Scholar 

  2. Gian Luca Cattani and Vladimiro Sassone. Higher dimensional transition systems. In Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science, pages 55–62, New Brunswick, New Jersey, 27–30 July 1996. IEEE Computer Society Press.

    Google Scholar 

  3. Søren Christensen, Hans Hüttel, and Colin Stirling. Bisimulation equivalence is decidable for all context-free processes. Information and Computation, 121(2):143–148, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  4. Sibylle Fröschle. Decidability of plain and hereditary history-preserving bisimilarity for BPP. Presented at 6th International Workshop on Expressiveness in Concurrency, EXPRESS’99, Eindhoven, The Netherlands, August 1999.

    Google Scholar 

  5. Sibylle Fröschle and Thomas Hildebrandt. On plain and hereditary history-preserving bisimulation. In Mirosław Kuty lowski, Leszek Pacholski, and Tomasz Wierzbicki, editors, Mathematical Foundations of Computer Science 1999, 24th International Symposium, MFCS’99, volume 1672 of LNCS, pages 354–365, Szklarska Poręba, Poland, September 6–10 1999. Springer.

    Chapter  Google Scholar 

  6. R. J. van Glabbeek. The linear time-branching time spectrum (Extended abstract). In J. C. M. Baeten and J. W. Klop, editors, CONCUR’ 90, Theories of Concurrency: Unification and Extension, volume 458 of LNCS, pages 278–297, Amsterdam, The Netherlands, 27–30 August 1990. Springer-Verlag.

    Chapter  Google Scholar 

  7. Rob van Glabbeek and Ursula Goltz. Equivalence notions for concurrent systems and refinement of actions (Extended abstract). In A. Kreczmar and G. Mirkowska, editors, Mathematical Foundations of Computer Science 1989, volume 379 of LNCS, pages 237–248, Porąbka-Kozubnik, Poland, August/September 1989. Springer-Verlag.

    Google Scholar 

  8. Jan Friso Groote and Hans Hüttel. Undecidable equivalences for basic process algebra. Information and Computation, 115(2):354–371, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  9. Matthew Hennessy and Robin Milner. Algebraic laws for nondeterminism and concurrency. Journal of the ACM, 32(1):137–161, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  10. Yoram Hirshfeld, Mark Jerrum, and Faron Moller. A polynomial algorithm for deciding bisimilarity of normed context-free processes. Theoretical Computer Science, 158(1–2):143–159, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  11. Lalita Jategaonkar and Albert R. Meyer. Deciding true concurrency equivalences on safe, finite nets. Theoretical Computer Science, 154:107–143, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  12. André Joyal, Mogens Nielsen, and Glynn Winskel. Bisimulation from open maps. Information and Computation, 127(2):164–185, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  13. Paris C. Kanellakis and Scott A. Smolka. CCS expressions, finite state processes, and three problems of equivalence. Information and Computation, 86(1):43–68, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  14. P. Madhusudan and P. S. Thiagarajan. Controllers for discrete event systems via morphisms. In Davide Sangiorgi and Robert de Simone, editors, CONCUR’98, Concurrency Theory, 9th International Conference, Proceedings, volume 1466 of LNCS, pages 18–33, Nice, France, September 1998. Springer.

    Chapter  Google Scholar 

  15. R. Milner. A Calculus of Communicating Systems, volume 92 of LNCS. Springer, 1980.

    MATH  Google Scholar 

  16. Faron Moller and Scott A. Smolka. On the computational complexity of bisimulation. ACM Computing Surveys, 27(2):287–289, 1995.

    Article  Google Scholar 

  17. Mogens Nielsen and Christian Clausen. Games and logics for a noninterleaving bisimulation. Nordic Journal of Computing, 2(2):221–249, 1995.

    MATH  MathSciNet  Google Scholar 

  18. Mogens Nielsen and Glynn Winskel. Petri nets and bisimulation. Theoretical Computer Science, 153(1–2):211–244, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  19. Robert Paige and Robert E. Tarjan. Three partition refinement algorithms. SIAM Journal on Computing, 16(6):973–989, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  20. D. M. R. Park. Concurrency and automata on infinite sequences. In P. Deussen, editor, Theoretical Computer Science: 5th GI-Conference, volume 104 of LNCS, pages 167–183. Springer-Verlag, 1981.

    Google Scholar 

  21. A. Rabinovich and B. Trakhtenbrot. Behaviour structures and nets of processes. Fundamenta Informaticae, 11:357–404, 1988.

    MATH  MathSciNet  Google Scholar 

  22. Walter Vogler. Deciding history preserving bisimilarity. In Javier Leach Albert, Burkhard Monien, and Mario Rodríguez-Artalejo, editors, Automata, Languages and Programming, 18th International Colloquium, ICALP’91, volume 510 of LNCS, pages 493–505, Madrid, Spain, 8–12 July 1991. Springer-Verlag.

    Google Scholar 

  23. Glynn Winskel and Mogens Nielsen. Models for concurrency. In S. Abramsky, Dov M. Gabbay, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science, volume 4, Semantic Modelling, pages 1–148. Oxford University Press, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Building 540, 8000, Aarhus C, Denmark

    Marcin Jurdziński & Mogens Nielsen

Authors
  1. Marcin Jurdziński
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mogens Nielsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany

    Horst Reichel

  2. Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France

    Sophie Tison

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jurdziński, M., Nielsen, M. (2000). Hereditary History Preserving Bisimilarity Is Undecidable. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_30

Download citation

  • DOI: https://doi.org/10.1007/3-540-46541-3_30

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation