Advertisement

A Constructive Proof of the Soundness of the Encoding of Random Access Machines in a Linda Calculus with Ordered Semantics

  • Claudio Sacerdoti Coen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2841)

Abstract

Random Access Machines (RAMs) are a deterministic Turing-complete formalism especially well suited for being encoded in other formalisms. This is due to the fact that RAMs can be defined starting from very primitive concepts and operations, which are unbounded natural numbers, tuples, successor, predecessor and test for equality to zero. Since these concepts are easily available also in theorem-provers and proof-assistants, RAMs are good candidates for proving Turing-completeness of formalisms using a proof-assistant. In this paper we describe an encoding in Coq of RAMs into a Linda Calculus endowed with the Ordered Semantics. We discuss the main difficulties that must be faced and the techniques we adopted to solve them.

Keywords

Parallel Composition Process Algebra Constructive Proof Program Counter Tuple Space 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Busi, N., Gorrieri, R., Zavattaro, G.: On the Expressiveness of Linda Coordination Primitives. Information and Computation 156(1/2), 90–121 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    The Coq proof-assistant, http://coq.inria.fr/
  3. 3.
    Hofmann, M.: Extensional concepts in intensional type theory. Ph.D. thesis, University of Edinburgh (July 1995)Google Scholar
  4. 4.
    McBride, C.: Dependently Typed Functional Programs and their Proofs. Ph.D. thesis, University of Edinburgh (2000)Google Scholar
  5. 5.
    Gelernter, D.: Generative Communication in Linda. ACM Transactions on Programming Languages and Systems 7(1), 80–112 (1985)zbMATHCrossRefGoogle Scholar
  6. 6.
    Gelernter, D., Carriero, N.: Coordination Languages and their Significance. Communications of the ACM 35(2), 97–102 (1992)CrossRefGoogle Scholar
  7. 7.
    Barthe, G., Courtieu, P.: Efficient Reasoning about executable specifications in Coq. In: Carreño, V.A., Muñoz, C.A., Tahar, S. (eds.) TPHOLs 2002. LNCS, vol. 2410, pp. 31–46. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Asperti, A., Guidi, F., Padovani, L., Sacerdoti Coen, C., Schena, I.: Mathematical Knowledge Management in HELM. In: On-Line Proceedings of the First International Workshop on Mathematical Knowledge Management (MKM 2001), RISCLinz, Austria (September 2001)Google Scholar
  9. 9.
    Asperti, A., Guidi, F., Padovani, L., Sacerdoti Coen, C., Schena, I.: XML, Stylesheets and the re-mathematization of Formal Content. In: On-Line Proceedings of EXTREME 2001 (2001)Google Scholar
  10. 10.
    Milner, R.: The Polyadic π-Calculus: A Tutorial Technical Report, Department of Computer Science, University of Edinburgh, ECS-LFCS-91-180 (October 1991)Google Scholar
  11. 11.
    Minsky, M.L.: Computation: finite and infinite machines. Prentice-Hall, Englewood Cliffs (1967)zbMATHGoogle Scholar
  12. 12.
    Shepherdson, J.C., Sturgis, J.E.: Computability of recursive functions. Journal of the ACM 10, 217–255 (1963)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Busi, N., Gorrieri, R., Zavattaro, G.: A Process Algebraic View of Linda Coordination Primitives. Theoretical Computer Science 192(2), 167–199 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Busi, N., Zavattaro, G.: On the Expressiveness of Movement in Pure Mobile Ambients. In: Gregori, E., Cherkasova, L., Cugola, G., Panzieri, F., Picco, G.P. (eds.) NETWORKING 2002. LNCS, vol. 2376, Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Claudio Sacerdoti Coen
    • 1
  1. 1.Department of Computer ScienceBolognaItaly

Personalised recommendations