Skip to main content

Ready to Preorder: Get Your BCCSP Axiomatization for Free!

  • Conference paper
Algebra and Coalgebra in Computer Science (CALCO 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4624))

Included in the following conference series:

Abstract

This paper contributes to the study of the equational theory of the semantics in van Glabbeek’s linear time - branching time spectrum over the language BCCSP, a basic process algebra for the description of finite synchronization trees. It offers an algorithm for producing a complete (respectively, ground-complete) equational axiomatization of any behavioral congruence lying between ready simulation equivalence and partial traces equivalence from a complete (respectively, ground-complete) inequational axiomatization of its underlying precongruence—that is, of the precongruence whose kernel is the equivalence. The algorithm preserves finiteness of the axiomatization when the set of actions is finite.

The first and third author were partly supported by the project “The Equational Logic of Parallel Processes” (nr. 060013021) of The Icelandic Research Fund.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Aceto, L., Bloom, B., Vaandrager, F.W.: Turning SOS rules into equations. Information and Computation 111(1), 1–52 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aceto, L., Fokkink, W., van Glabbeek, R.J., Ingolfsdottir, A.: Nested semantics over finite trees are equationally hard. Information and Computation 191(2), 203–232 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Aceto, L., Fokkink, W., Ingolfsdottir, A.: A menagerie of non-finitely based process semantics over BPA*—from ready simulation to completed traces. Mathematical Structures in Computer Science 8(3), 193–230 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Aceto, L., Fokkink, W., Ingolfsdottir, A.: Ready to preorder: Get your BCCSP axiomatization for free! Report RS-07-3, BRICS Research Series (2007)

    Google Scholar 

  5. Aceto, L., Fokkink, W., Ingolfsdottir, A., Luttik, B.: Finite equational bases in process algebra: Results and open questions. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 338–367. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Blom, S., Fokkink, W., Nain, S.: On the axiomatizability of ready traces, ready simulation and failure traces. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 109–118. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  8. Chen, T., Fokkink, W.: On finite alphabets and infinite bases III: Simulation. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 421–434. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Chen, T., Fokkink, W., Nain, S.: On finite alphabets and infinite bases II: Completed and ready simulation. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006 and ETAPS 2006. LNCS, vol. 3921, pp. 1–15. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Fokkink, W., Nain, S.: A finite basis for failure semantics. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 755–765. Springer, Heidelberg (2005)

    Google Scholar 

  11. de Frutos-Escrig, D., Gregorio-Rodríguez, C.: Bisimulations up-to for the linear time branching time spectrum. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 278–292. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. de Frutos-Escrig, D., Gregorio-Rodríguez, C.: Simulations up-to and canonical preorders (extended abstract). In: Proc. SOS 2007, ENTCS, Elsevier (to appear)

    Google Scholar 

  13. van Glabbeek, R.J.: The linear time – branching time spectrum I. The semantics of concrete, sequential processes. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, pp. 3–99. Elsevier, Amsterdam (2001)

    Google Scholar 

  14. Groote, J.F.: A new strategy for proving ω-completeness with applications in process algebra. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 314–331. Springer, Heidelberg (1990)

    Google Scholar 

  15. Groote, J.F., Vaandrager, F.W.: Structured operational semantics and bisimulation as a congruence. Information and Computation 100, 202–260 (1992)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  17. Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)

    MATH  Google Scholar 

  18. Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)

    MATH  Google Scholar 

  19. Moller, F.: Axioms for Concurrency. PhD thesis, Department of Computer Science, University of Edinburgh (July 1989)

    Google Scholar 

  20. Rounds, W., Brookes, S.: Possible futures, acceptances, refusals and communicating processes. In: Proc. FOCS 1981, pp. 140–149. IEEE Computer Society Press, Los Alamitos (1981)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Till Mossakowski Ugo Montanari Magne Haveraaen

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Aceto, L., Fokkink, W., Ingólfsdóttir, A. (2007). Ready to Preorder: Get Your BCCSP Axiomatization for Free! . In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds) Algebra and Coalgebra in Computer Science. CALCO 2007. Lecture Notes in Computer Science, vol 4624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73859-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73859-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73857-2

  • Online ISBN: 978-3-540-73859-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics