Skip to main content

Rule Formats for Distributivity

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6638)

Abstract

This paper proposes rule formats for Structural Operational Semantics guaranteeing that certain binary operators are left distributive with respect to a set of binary operators. Examples of left-distributivity laws from the literature are shown to be instances of the provided formats.

Keywords

  • Composition Operator
  • Rule Format
  • Operational Semantic
  • Parallel Composition
  • Process Algebra

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The work of Aceto, Cimini and Ingolfsdottir has been partially supported by the projects ‘New Developments in Operational Semantics’ (nr. 080039021) and ‘Meta-theory of Algebraic Process Theories’ (nr. 100014021) of the Icelandic Research Fund. The work on the paper was partly carried out while Luca Aceto held an Abel Extraordinary Chair at Universidad Complutense de Madrid, Spain, supported by the NILS Mobility Project.

This is a preview of subscription content, access via your institution.

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aceto, L., Cimini, M., Ingolfsdottir, A., Mousavi, M.R., Reniers, M.A.: Rule formats for distributivity. Technical Report CSR-10-16, TU/Eindhoven (2010)

    Google Scholar 

  2. Aceto, L., Ingolfsdottir, A., Mousavi, M.R., Reniers, M.A.: Algebraic properties for free! Bulletin of the European Association for Theoretical Computer Science 99, 81–104 (2009); Columns: Concurrency

    MATH  Google Scholar 

  3. Aceto, L., Birgisson, A., Ingolfsdottir, A., Mousavi, M.R., Reniers, M.A.: Rule formats for determinism and idempotence. In: Arbab, F., Sirjani, M. (eds.) FSEN 2009. LNCS, vol. 5961, pp. 146–161. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  4. Aceto, L., Bloom, B., Vaandrager, F.W.: Turning SOS rules into equations. Inf. Comput. 111(1), 1–52 (1994)

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Aceto, L., Cimini, M., Ingolfsdottir, A., Mousavi, M.R., Reniers, M.A.: On rule formats for zero and unit elements. In: Proceedings of the 26th Conference on the Mathematical Foundations of Programming Semantics (MFPS XXVI), Ottawa, Canada. Electronic Notes in Theoretical Computer Science, vol. 265, pp. 145–160. Elsevier B.V., The Netherlands (2010)

    Google Scholar 

  6. 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)

    CrossRef  Google Scholar 

  7. Aceto, L., Fokkink, W., Verhoef, C.: Structural operational semantics. In: Handbook of Process Algebra, pp. 197–292. Elsevier, Amsterdam (2001)

    CrossRef  Google Scholar 

  8. Aceto, L., Ingolfsdottir, A., Mousavi, M.R., Reniers, M.A.: Rule formats for unit elements. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds.) SOFSEM 2010. LNCS, vol. 5901, pp. 141–152. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  9. Baeten, J., Bergstra, J.: Mode transfer in process algebra. Technical Report Report CSR 00–01, Eindhoven University of Technology (2000)

    Google Scholar 

  10. Baeten, J., Bergstra, J., Klop, J.W.: Syntax and defining equations for an interrupt mechanism in process algebra. Fundamenta Informaticae IX(2), 127–168 (1986)

    MathSciNet  MATH  Google Scholar 

  11. Baeten, J., Basten, T., Reniers, M.A.: Process Algebra: Equational Theories of Communicating Processes. Cambridge Tracts in Theoretical Computer Science, vol. 50. Cambridge University Press, Cambridge (2009)

    CrossRef  MATH  Google Scholar 

  12. Baeten, J., Mauw, S.: Delayed choice: An operator for joining Message Sequence Charts. In: Hogrefe, D., Leue, S. (eds.) Formal Description Techniques VII, Proceedings of the 7th IFIP WG6.1 International Conference on Formal Description Techniques, Berne, Switzerland. IFIP Conference Proceedings, vol. 6, pp. 340–354. Chapman & Hall, Boca Raton (1995)

    CrossRef  Google Scholar 

  13. Bergstra, J., Klop, J.W.: Fixed point semantics in process algebras. Report IW 206, Mathematisch Centrum, Amsterdam (1982)

    Google Scholar 

  14. Brinksma, E.: A tutorial on LOTOS. In: Proceedings of the IFIP WG6.1 Fifth International Conference on Protocol Specification, Testing and Verification V, pp. 171–194. North-Holland Publishing Co., Amsterdam (1985)

    Google Scholar 

  15. Cranen, S., Mousavi, M.R., Reniers, M.A.: A rule format for associativity. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 447–461. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  16. Hoare, C.: Communicating Sequential Processes. Prentice-Hall International, Englewood Cliffs (1985)

    MATH  Google Scholar 

  17. Milner, R.: Communication and Concurrency. Prentice-Hall, Inc., Upper Saddle River (1989)

    MATH  Google Scholar 

  18. Moller, F.: The importance of the left merge operator in process algebras. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 752–764. Springer, Heidelberg (1990)

    CrossRef  Google Scholar 

  19. Mousavi, M.R., Reniers, M.A., Groote, J.F.: A syntactic commutativity format for SOS. Information Processing Letters 93, 217–223 (2005)

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Mousavi, M.R., Reniers, M.A., Groote, J.F.: SOS formats and meta-theory: 20 years after. Theor. Comput. Sci. 373(3), 238–272 (2007)

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Nicollin, X., Sifakis, J.: The algebra of timed processes, ATP: Theory and application. Information and Computation 114(1), 131–178 (1994)

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. Plotkin, G.D.: A structural approach to operational semantics. J. Log. Algebr. Program. 60-61, 17–139 (2004)

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. Przymusinski, T.: The well-founded semantics coincides with the three-valued stable semantics. Fundamenta Informaticae 13(4), 445–463 (1990)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Aceto, L., Cimini, M., Ingolfsdottir, A., Mousavi, M.R., Reniers, M.A. (2011). Rule Formats for Distributivity. In: Dediu, AH., Inenaga, S., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2011. Lecture Notes in Computer Science, vol 6638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21254-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21254-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21253-6

  • Online ISBN: 978-3-642-21254-3

  • eBook Packages: Computer ScienceComputer Science (R0)