Skip to main content
SpringerLink
Log in

Multiset Rewriting: A Semantic Framework for Concurrency with Name Binding

  • Conference paper
Rewriting Logic and Its Applications (WRLA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6381))

Included in the following conference series:

  • 430 Accesses

Abstract

We revise multiset rewriting with name binding, by combining the two main existing approaches to the study of concurrency by means of multiset rewriting: multiset rewriting with existential quantification and constrained multiset rewriting. We obtain ν-MSRs, where we rewrite multisets of atomic formulae, in which some names may be restricted. We prove that ν-MSRs are equivalent to a class of Petri nets in which tokens are tuples of pure names, called pν-APNs. Then we encode π-calculus processes into ν-MSRs in a very direct way, that preserves the topology of bound names, by using the concept of derivatives of a π-calculus process. Finally, we discuss how the recent results on decidable subclasses of the π-calculus are independent of the particular reaction rule of the π-calculus, so that they can be obtained in the more general framework of ν-MSRs. Thus, those results carry over not only to the π-calculus, but to any other formalism that can be encoded within it, as pν-APNs.

Work partially supported by the Spanish projects DESAFIOS10 TIN2009-14599-C03-01 and PROMETIDOS S2009/TIC-1465.

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 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. Abadi, M., Gordon, A.D.: A Calculus for Cryptographic Protocols: The spi Calculus. Inf. Comput. 148(1), 1–70 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Abdulla, P.A., Delzanno, G., Begin, L.V.: Comparing the expressive power of well-structured transition systems. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 99–114. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Baldan, P., Bonchi, F., Gadducci, F.: Encoding asynchronous interactions using open Petri nets. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 99–114. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Boudol, G.: Some chemical abstract machines. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1993. LNCS, vol. 803, pp. 92–123. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  5. Busi, N., Gorrieri, R.: Distributed semantics for the pi-calculus based on Petri nets with inhibitor arcs. J. Log. Algebr. Program. 78(3), 138–162 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Busi, N., Zavattaro, G.: Deciding reachability problems in turing-complete fragments of mobile ambients. Mathematical Structures in Computer Science 19(6), 1223–1263 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cardelli, L., Gordon, A.D.: Mobile ambients. Theor. Comput. Sci. 240(1), 177–213 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cervesato, I.: Typed MSR: Syntax and Examples. In: Gorodetski, V.I., Skormin, V.A., Popyack, L.J. (eds.) MMM-ACNS 2001. LNCS, vol. 2052, pp. 159–177. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Cervesato, I., Durgin, N.A., Lincoln, P., Mitchell, J.C., Scedrov, A.: A meta-notation for protocol analysis. In: CSFW, pp. 55–69 (1999)

    Google Scholar 

  10. Ciancia, V., Montanari, U.: A name abstraction functor for named sets. Electr. Notes Theor. Comput. Sci. 203(5), 49–70 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. de Bruijn, N.: Lambda calculus with nameless dummies, a tool for automatic formula manipulation, with application to the church-rosser theorem. In: Proceedings Kninkl. Nederl. Akademie van Wetenschappen, vol. 75, pp. 381–392 (1972)

    Google Scholar 

  12. Delzanno, G.: An overview of MSR(C): A CLP-based framework for the symbolic verification of parameterized concurrent systems. Electr. Notes Theor. Comput. Sci. 76 (2002)

    Google Scholar 

  13. Delzanno, G.: Constraint multiset rewriting. Technical Report DISI-TR-05-08, University of Genova (2005)

    Google Scholar 

  14. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theor. Comput. Sci. 256(1-2), 63–92 (2001)

    MathSciNet  MATH  Google Scholar 

  15. Gadducci, F., Miculan, M., Montanari, U.: About permutation algebras, (pre) sheaves and named sets. Higher-Order and Symbolic Computation 19(2-3), 283–304 (2006)

    Article  MATH  Google Scholar 

  16. Gordon, A.D.: Notes on nominal calculi for security and mobility. In: Focardi, R., Gorrieri, R. (eds.) FOSAD 2000. LNCS, vol. 2171, pp. 262–330. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  17. Lazic, R., Newcomb, T., Ouaknine, J., Roscoe, A.W., Worrell, J.: Nets with tokens which carry data. Fundam. Inform. 88(3), 251–274 (2008)

    MathSciNet  MATH  Google Scholar 

  18. Meseguer, J.: Rewriting logic as a semantic framework for concurrency: a progress report. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 331–372. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  19. Meseguer, J., Montanari, U.: Petri nets are monoids. Inf. Comput. 88(2), 105–155 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  20. Meyer, R.: On boundedness in Depth in the pi-calculus. In: Ausiello, G., Karhumäki, J., Mauri, G., Ong, C.H.L. (eds.) IFIP TCS. LNCS, vol. 273, pp. 477–489. Springer, Heidelberg (1987)

    Google Scholar 

  21. Meyer, R.: A theory of structural stationarity in the pi-calculus. Acta Inf 46(2), 87–137 (2009)

    Article  MATH  Google Scholar 

  22. Meyer, R., Gorrieri, R.: On the relationship between pi-calculus and finite place/transition Petri nets. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 463–480. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  23. Rosa-Velardo, F., de Frutos-Escrig, D.: Name creation vs. replication in Petri net systems. Fundam. Inform. 88(3), 329–356 (2008)

    MathSciNet  MATH  Google Scholar 

  24. Rosa-Velardo, F., de Frutos-Escrig, D.: Decidability problems in Petri nets with name creation and replication (submitted)

    Google Scholar 

  25. Rosa-Velardo, F., de Frutos-Escrig, D., Alonso, O.M.: On the expressiveness of Mobile Synchronizing Petri Nets. Electr. Notes Theor. Comput. Sci. 180(1), 77–94 (2007)

    Article  MATH  Google Scholar 

  26. Rosa-Velardo, F., Segura, C., Verdejo, A.: Typed mobile ambients in Maude. Electr. Notes Theor. Comput. Sci. 147(1), 135–161 (2006)

    Article  MATH  Google Scholar 

  27. Sangiorgi, D., Walker, D.: The pi-calculus: a Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  28. Stehr, M.O.: CINNI - a generic calculus of explicit substitutions and its application to lambda-, varsigma- and pi-calculi. Electr. Notes Theor. Comput. Sci. 36 (2000)

    Google Scholar 

  29. Stehr, M.O., Meseguer, J., Ölveczky, P.C.: Rewriting logic as a unifying framework for Petri nets. In: Ehrig, H., Juhás, G., Padberg, J., Rozenberg, G. (eds.) APN 2001. LNCS, vol. 2128, pp. 250–303. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  30. Thati, P., Sen, K., Martí-Oliet, N.: An executable specification of asynchronous pi-calculus semantics and may testing in Maude 2.0. Electr. Notes Theor. Comput. Sci. 71 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dpto. de Sistemas Informáticos y Computación, Universidad Complutense de Madrid, Spain

    Fernando Rosa-Velardo

Authors
  1. Fernando Rosa-Velardo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Gaustadalléen 23, 0373, Oslo, Norway

    Peter Csaba Ölveczky

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rosa-Velardo, F. (2010). Multiset Rewriting: A Semantic Framework for Concurrency with Name Binding. In: Ölveczky, P.C. (eds) Rewriting Logic and Its Applications. WRLA 2010. Lecture Notes in Computer Science, vol 6381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16310-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16310-4_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16309-8

  • Online ISBN: 978-3-642-16310-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation