Distributed Computing

, Volume 23, Issue 1, pp 61–83 | Cite as

A spatial equational logic for the applied π-calculus

  • Étienne LozesEmail author
  • Jules Villard


Spatial logics have been proposed to reason locally and modularly on algebraic models of distributed systems. In this paper we define the spatial equational logic A π L whose models are processes of the applied π-calculus. This extension of the π-calculus allows term manipulation and records communications as aliases in a frame, thus augmenting the predefined underlying equational theory. Our logic allows one to reason locally either on frames or on processes, thanks to static and dynamic spatial operators. We study the logical equivalences induced by various relevant fragments of A π L, and show in particular that the whole logic induces a coarser equivalence than structural congruence. We give characteristic formulae for some of these equivalences and for static equivalence. Going further into the exploration of A π L’s expressivity, we also show that it can eliminate standard term quantification.


Spatial Logic Applied pi-calculus 


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  1. 1.
    Abadi M., Cortier V.: Deciding knowledge in security protocols under equational theories. Theor. Comput. Sci. 367(1–2), 2–32 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Abadi, M., Fournet, C.: Mobile values, new names, and secure communication. In: POPL’01, pp. 104–115 (2001)Google Scholar
  3. 3.
    Acciai, L., Boreale, M.: Deciding safety properties in infinite-state pi-calculus via behavioural types. In: Proceedings of ICALP’2009 Volume 5556 of Lecture Notes in Computer Science, pp. 31–42, (2009)Google Scholar
  4. 4.
    Acciai, L., Boreale, M., Zavattaro, G.: On the relationship between spatial logics and behavioral simulations. In: Proceedings of FOSSACS 2010 Volume 6014 of Lecture Notes in Computer Science, pp. 146–160, (2010)Google Scholar
  5. 5.
    Blanchet, B.: Automatic proof of strong secrecy for security protocols. In: IEEE Symposium on Security and Privacy, pp. 86–100, Oakland, California (2004)Google Scholar
  6. 6.
    Blanchet, B., Abadi, M., Fournet, C.: Automated verification of selected equivalences for security protocols. In: LICS 2005, pp. 331–340 (2005)Google Scholar
  7. 7.
    Borgström J.: Static equivalence is harder than knowledge. Electron. Notes Theor. Comput. Sci. 154(3), 45–57 (2006)CrossRefGoogle Scholar
  8. 8.
    Caires, L., Cardelli, L.: A spatial logic for concurrency (part I). J. Inf. Comput. 186(2), (2003)Google Scholar
  9. 9.
    Caires, L., Lozes, É.: Elimination of quantifiers and undecidability in spatial logics for concurrency. In: CONCUR Volume 3170 of LNCS, pp. 240–257. Springer, London (2004)Google Scholar
  10. 10.
    Calcagno, C., Cardelli, L., Gordon, A.D.: Deciding validity in a spatial logic for trees. In: Shao, Z., Lee, P. (eds.) TLDI, pp. 62–73. ACM, (2003)Google Scholar
  11. 11.
    Calcagno, C., Gardner, P., Zarfaty, U.: Context logic and tree update. In: Palsberg, J., Abadi, M. (eds.) POPL, pp. 271–282. ACM, (2005)Google Scholar
  12. 12.
    Delaune, S., Kremer, S., Ryan, M.D.: Coercion-resistance and receipt-freeness in electronic voting. In: Proceedings of the 19th IEEE Computer Security Foundations Workshop (CSFW’06), pp. 28–39, Venice, Italy, July 2006. IEEE Computer Society Press (2006)Google Scholar
  13. 13.
    Gabbay M.J., Pitts A.M.: A new approach to abstract syntax with variable binding. Formal Aspects Comput. 13(3), 341–363 (2002)zbMATHCrossRefGoogle Scholar
  14. 14.
    Gordon, A., Cardelli, L.: Anytime, anywhere: modal logics for mobile ambients. In: ACM Press editor (ed.) POPL 2000, pp. 365–377, (2000)Google Scholar
  15. 15.
    Hirschkoff, D.: An extensional spatial logic for mobile processes. In: CONCUR’02 Volume 3252 of LNCS. Springer, (2002)Google Scholar
  16. 16.
    Hirschkoff, D., Lozes, É., Sangiorgi, D.: Minimality results for spatial logics. In: FSTTCS’03 Volume 2914 of LNCS, Mumbai, India, pp. 252–264. Springer (2003)Google Scholar
  17. 17.
    Hirschkoff, D., Lozes, É., Sangiorgi, D.: On the expressiveness of the ambient logic. Logical Methods Comput. Sci. 2(2) (2006)Google Scholar
  18. 18.
    Hirschkoff, D., Lozes, É., Sangiorgi, D.: On the expressiveness of the ambient logic. Logical Methods Comput. Sci. 4(4) (2008)Google Scholar
  19. 19.
    Hüttel H., Pedersen M.D.: A logical characterisation of static equivalence. Electron. Notes Theor. Comput. Sci. 173, 139–157 (2007)CrossRefGoogle Scholar
  20. 20.
    Jacquemard, F., Lozes, E., Treinen, R., Villard, J.: First-order constraint systems with multiple congruence relations. (submitted)Google Scholar
  21. 21.
    Kramer, S.: Logical concepts in cryptography. PhD thesis, École Polytechnique F édérale de Lausanne, (2007)Google Scholar
  22. 22.
    Lozes, É., Villard, J.: A spatial equational logic for the applied π-calculus. In: van Breugel, F., Chechik, M. (eds.) Proceedings of the 19th International Conference on Concurrency Theory (CONCUR’08) Volume 5201 of Lecture Notes in Computer Science, pp. 387–401, Toronto, Canada. Springer 2008Google Scholar
  23. 23.
    Mardare, R.: Observing distributed computation. A dynamic-epistemic approach. In: CALCO Volume 4624 of LNCS, pp. 379–393. Springer, (2007)Google Scholar
  24. 24.
    Milner R., Parrow J., Walker D.: A calculus of mobile processes, i. Inf. Comput. 100(1), 1–40 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Pym D.J., Tofts C.M.N.: A Calculus and logic of resources and processes. Formal Aspects Comput. 18(4), 495–517 (2006)zbMATHCrossRefGoogle Scholar
  26. 26.
    Reynolds, J.C.: Separation logic: a logic for shared mutable data structures. In 17th IEEE Symposium on Logic in Computer Science (LICS), pp. 55–74, (2002)Google Scholar
  27. 27.
    Sangiorgi, D.: Extensionality and intensionality of the ambient logics. In: POPL (2001)Google Scholar
  28. 28.
    Villard, J., Lozes, É., Treinen, R.: A spatial equational logic for the applied pi-calculus. Research report LSV-08-10, LSV, ENS Cachan, France. 44 pp. (2008)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.LSV, ENS CachanCachanFrance

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