A fundamental theorem of asynchronous parallel computation

  • Robert M. Keller
Session 3: Modelling And Parallelism Detection
Part of the Lecture Notes in Computer Science book series (LNCS, volume 24)


A recurrent phenomenon in models of asynchronous parallel computation is expressed in an abstract model. Many previous models, or special cases thereof, possess three local properties: determinism, commutativity, and persistence, as they are defined here. We show that the possession of these local properties by a system is a sufficient condition for the possession of the global confluence or "Church-Rosser" property. The relation of this property to the "determinacy" of asynchronous systems was suggested in recent work by Rosen. We show that determinacy proofs for many models, and proofs of some other properties of interest, are really corollaries of the main theorem of this paper.


Transition System Asynchronous System Asynchronous Circuit Recurrent Phenomenon Shared Queue 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. Adams, "A Computation Model with Data Flow Sequencing", Tech. Report CS 117 (Ph.D. dissertation), Computer Science Dept., Stanford Univ. (Dec. 1968).Google Scholar
  2. [2]
    F. Commoner, A.W. Holt, S. Even, and A. Pnueli, "Marked Directed Graphs", J. Computer and System Sciences, 5, 5 (Oct. 1971) pp. 511–523Google Scholar
  3. [3]
    M. Hack, "Decision Problems for Petri Nets and Vector Addition Systems", MIT Project MAC, Computation Structures Group Memo 95 (Mar. 1974).Google Scholar
  4. [4]
    G. Kahn, "A Preliminary Theory for Parallel Programs", IRIA Research Report No. 6, (Jan. 1973).Google Scholar
  5. [5]
    R.M. Karp, and R.E. Miller, "Parallel Program Schemata," J. Computer and System Sciences, 3, 2, (May 1969), pp. 147–195.Google Scholar
  6. [6]
    R.M. Karp, and R.E. Miller, "Properties of a Model for Parallel Computations: Determinacy, Termination, and Queuing," SIAM J. Applied Math., 14, 6. (Nov. 1966), pp. 1390–1411.Google Scholar
  7. [7]
    R.M. Keller, "Parallel Program Schemata and Maximal Parallelism," J. ACM, 20, 3, (July 1973) pp. 514–537 and 20, 4, (Oct. 1973) pp. 696–710.Google Scholar
  8. [8]
    R.M. Keller, "Vector Replacement Systems: A Formalism for Modeling Asynchronous Systems," Tech. Rept. 117, Computer Science Laboratory, Princeton University (Jan. 1974).Google Scholar
  9. [9]
    F.L. Luconi, "Asynchronous Computational Structures," MIT Project MAC Rept. MAC-TR-49 (1968).Google Scholar
  10. [10]
    D.E. Muller and W.S. Bartky, "A Theory of Asynchronous Circuits," Annals of the Computation Laboratory of Harvard University, 29, Pt. 1, (1959) pp. 204–243.Google Scholar
  11. [11]
    M.H.A. Newman, "On Theories with a Combinatorial Definition of ‘Equivalence'" Annals of Math., 43, 2, (April 1942), pp. 223–243.Google Scholar
  12. [12]
    S. Patil, "Closure Properties of Interconnections of Determinate Systems," Proc. Project MAC Conference on Concurrent Systems and Parallel Computations, (June 1970), pp. 107–116.Google Scholar
  13. [13]
    B. Rosen, "Tree Manipulating Systems and Church-Rosser Theorems", J. ACM 20, 1, (Jan. 1973), pp. 160–187.Google Scholar
  14. [14]
    R. Sethi, "Theorems of Confluence for Unions of Replacement Systems with Equivalences," Tech. Rept. 131, Computer Science Dept., Pennsylvania State University (Oct. 1972).Google Scholar
  15. [15]
    R.C. Holt, "On Deadlock in Computer Systems," Univ. of Toronto Computer Science Research Group Rept. CSRG-6, (April 1971).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Robert M. Keller
    • 1
  1. 1.Department of Electrical EngineeringPrinceton UniversityPrinceton

Personalised recommendations