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Interpreting a Finitary Pi-calculus in Differential Interaction Nets

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CONCUR 2007 – Concurrency Theory (CONCUR 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4703))

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Abstract

We propose and study a translation of a pi-calculus without sums nor replication/recursion into an untyped and essentially promotion-free version of differential interaction nets. We define a transition system of labeled processes and a transition system of labeled differential interaction nets. We prove that our translation from processes to nets is a bisimulation between these two transition systems. This shows that differential interaction nets are sufficiently expressive for representing concurrency and mobility, as formalized by the pi-calculus.

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References

  1. Amadio, R., Curien, P.-L.: Domains and lambda-calculi. Cambridge Tracts in Theoretical Computer Science, vol. 46. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  2. Abramsky, S., Melliès, P.-A.: Concurrent games and full completeness. In: Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, Los Alamitos (1999)

    Google Scholar 

  3. Beffara, E.: Logique, Réalisabilité et Concurrence. PhD thesis, Université Denis Diderot (2005)

    Google Scholar 

  4. Berger, M., Honda, K., Yoshida, N.: Strong normalisability in the pi-calculus. Information and Computation (2003) (to appear)

    Google Scholar 

  5. Beffara, E., Maurel, F.: Concurrent nets: a study of prefixing in process calculi, vol. 356. Theoretical Computer Science (2005)

    Google Scholar 

  6. Curien, P.-L., Faggian, C.: An approach to innocent strategies as graphs. Technical report, Preuves, Programmes et Systèmes, Submitted for publication (2006)

    Google Scholar 

  7. Ehrhard, T.: Finiteness spaces. Mathematical Structures in Computer Science 15(4), 615–646 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ehrhard, T., Laurent, O.: Acyclic solos (submitted, 2007)

    Google Scholar 

  9. Ehrhard, T., Regnier, L.: Differential interaction nets. Theoretical Computer Science (2006) (to appear)

    Google Scholar 

  10. Engberg, U., Winskel, G.: Completeness results for linear logic on petri nets. Annals of Pure and Applied Logic 86(2), 101–135 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Faggian, C., Maurel, F.: Ludics nets, a game model of concurrent interaction. In: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science, pp. 376–385. IEEE Computer Society, Los Alamitos (2005)

    Google Scholar 

  12. Girard, J.-Y.: Linear logic. Theoretical Computer Science 50, 1–102 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  13. Girard, J.-Y.: Normal functors, power series and the λ-calculus. Annals of Pure and Applied Logic 37, 129–177 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  14. Honda, K., Laurent, O.: An exact correspondence between a typed π-calculus and polarized proof-nets (2007) (in preparation)

    Google Scholar 

  15. Jensen, O., Milner, R.: Bigraphs and mobile processes (revised). Technical report, Cambridge University Computer Laboratory (2004)

    Google Scholar 

  16. Lafont, Y.: From proof nets to interaction nets. In: Girard, J.-Y., Lafont, Y., Regnier, L. (eds.) Advances in Linear Logic, pp. 225–247. Cambridge University Press, Cambridge (1995), Proceedings of the Workshop on Linear Logic, Ithaca, New York, June 1993

    Google Scholar 

  17. Laneve, C., Parrow, J., Victor, B.: Solo diagrams. In: Kobayashi, N., Pierce, B.C. (eds.) TACS 2001. LNCS, vol. 2215, Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  18. Laneve, C., Victor, B.: Solos in concert. Mathematical Structures in Computer Science 13(5), 657–683 (2003)

    Article  MathSciNet  Google Scholar 

  19. Mazza, D.: Multiport interaction nets and concurrency. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 21–35. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Melliès, P.-A.: Asynchronous games 2: the true concurrency of innocence. Theoretical Computer Science 358(2), 200–228 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  21. Milner, R.: The polyadic pi-calculus: a tutorial. In: Logic and Algebra of Specification, pp. 203–246. Springer, Heidelberg (1993)

    Google Scholar 

  22. Plotkin, G.: A powerdomain construction. SIAM Journal of Computing 5(3), 452–487 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  23. Regnier, L.: Lambda-Calcul et Réseaux. Thèse de doctorat, Université Paris 7 (January 1992)

    Google Scholar 

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

    MATH  Google Scholar 

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Luís Caires Vasco T. Vasconcelos

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Ehrhard, T., Laurent, O. (2007). Interpreting a Finitary Pi-calculus in Differential Interaction Nets. In: Caires, L., Vasconcelos, V.T. (eds) CONCUR 2007 – Concurrency Theory. CONCUR 2007. Lecture Notes in Computer Science, vol 4703. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74407-8_23

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  • DOI: https://doi.org/10.1007/978-3-540-74407-8_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74406-1

  • Online ISBN: 978-3-540-74407-8

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