PEI: a single unifying model to design parallel programs

  • E. Violard
  • G. -R. Perrin
Paper Sessions Specification, Verification
Part of the Lecture Notes in Computer Science book series (LNCS, volume 694)


A lot of programming models have been proposed to deal with parallelism in order to express program transformations and refinements. This justifies to introduce an unifying theory to abstract different concepts. The aim of this paper is to introduce such a theory. This theory includes the definitions of problems, programs and transformation rules. It is founded on the simple mathematical concepts of multiset and of an equivalence between their representations as data fields. Program transformations are founded on this equivalence and defined from a refinement relation. Due to the unifying aspect of this theory, solutions that can be reached by these transformations are relevant to various synchronous or asynchronous computing models.


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  1. [CCL91]
    M. Chen, Y. Choo, and J. Li. Parallel Functional Languages and Compilers. Frontier Series. ACM Press, 1991. chapter 7.Google Scholar
  2. [CM88]
    K.M. Chandy and J. Misra. Parallel Program Design: A foundation. Addison Wesley, 1988.Google Scholar
  3. [CMP92]
    P. Clauss, C. Mongenet, and G.-R. Perrin. Synthesis of size-optimal toroidal arrays for the algebraic path problem: A new contribution. Parallel Computing, 18:185–194, 1992.CrossRefGoogle Scholar
  4. [Cre91]
    C. Creveuil. Techniques d'analyse et de mise en oeuvre des programmes Gamma. PhD thesis, Université de Rennes 1, Décembre 1991.Google Scholar
  5. [INR91]
    INRIA Sophia-Antipolis, Valbonne. Centaur 1.1, 1991.Google Scholar
  6. [KMW67]
    R.M. Karp, R.E. Miller, and S. Winograd. The organization of computations for uniform recurrence equations. Journal of ACM, 14(3):563–590, Juillet 1967.Google Scholar
  7. [Mau89]
    C. Mauras. Alpha; un langage équationnel pour la conception et la programmation d'architectures parallèles synchrones. PhD thesis, Université de Rennes 1, Décembre 1989.Google Scholar
  8. [Mis90]
    J. Misra. Equational reasoning about nondeterministic processes. Formal Aspects of Computing, 2:167–195, 1990.CrossRefGoogle Scholar
  9. [Mor90]
    C. Morgan. Programming from specifications. C.A.R. Hoare. Prentice Hall Ed., Endlewood Cliffs, N.J., 1990.Google Scholar
  10. [Qui89]
    P. Quinton. The mapping of linear recurrence equations on regular arrays. Journal of VLSI Signal Processing, 1, 1989.Google Scholar
  11. [Vio92]
    E. Violard. Une théorie unificatrice pour la construction de programmes parallèles par des techniques de transformations. PhD thesis, Université de Franche-Comté, Octobre 1992.Google Scholar
  12. [VP92]
    E. Violard and G.-R. Perrin. Pei: a language and its refinement calculus for parallel programming. Parallel Computing, 18:1167–1184, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • E. Violard
    • 1
  • G. -R. Perrin
    • 1
  1. 1.Laboratoire d'InformatiqueUniversity of Franche-ComtéBesançon cedex

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