A uniform universal CREW PRAM

  • Bruno Martin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)


The universality of the Parallel Random-Access Machines is usually defined by simulating universal Turing machines or boolean networks. These definitions are well-suited if we are interested in evaluating the complexity of algorithms but it is not as good if we want to deal with computability. We propose in this paper another definition for the universality of the Parallel Random-Access Machines based on cellular automata and we discuss the advantages and the drawbacks of this simulation. We prove that there exists a Concurrent-Read Exclusive-Write Parallel Random-Access Machine which is capable of simulating any given cellular automaton in constant time. We then derive to the definition of complexity classes for the Parallel Random-Access Machines and for cellular automata.


Cellular Automaton Turing Machine Global Memory Boolean Network Cellular Automaton Model 
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  1. 1.
    J. Albert and K. Culik II. A simple universal cellular automaton and its one-way and totalistic version. Complex Systems, 1:1–16, 1987.Google Scholar
  2. 2.
    J. L. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity II. Springer Verlag, 1990.Google Scholar
  3. 3.
    Y. Feldman and E. Shapiro. Spatial machines, a more realistic approach to parallel computation. Communications of the ACM, 35(10):61–73, 1992.Google Scholar
  4. 4.
    T. Hagerhup. Fast and optimal simulations between CRCW PRAMs. In STACS '92, Lecture Notes in Computer Science, pages 45–56. Springer Verlag, 1992.Google Scholar
  5. 5.
    R. M. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. In Handbook of Theoretical Computer Science, volume A, chapter 17. Elsevier, 1990.Google Scholar
  6. 6.
    M. Machtey and P. Young. An introduction to the general theory of algorithms. Theory of computation series, North Holland, 1978.Google Scholar
  7. 7.
    J. Mahajan and K. Krithivasan. Relativised cellular automata and complexity classes. In S. Biswas and K. V. Nori, editors, FSTCS, Lecture Notes in Computer Science. Springer Verlag, 1991.Google Scholar
  8. 8.
    B. Martin. Efficient unidimensional universal cellular automaton. In Proceedings of the Mathematical Foundations of Computer Science. Springer Verlag, August 1992.Google Scholar
  9. 9.
    B. Martin. Construction modulaire d'automates cellulaires. PhD thesis, Ecole Normale Supérieure de Lyon, 1993.Google Scholar
  10. 10.
    B. Martin. A universal cellular automaton in quasi-linear time and its s-m-n form. Theoretical Computer Science, 123, 1994. To be published.Google Scholar
  11. 11.
    H. Rogers. Theory of recursive functions and effective computability. Mc Graw-Hill, 1967.Google Scholar
  12. 12.
    R. Sommerhadler and S.C. van Westrhenen. The Theory of Computability, Programs, Machines, Effectiveness and Feasibility. Addison Wesley, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Bruno Martin
    • 1
  1. 1.Ecole Normale Supérieure de LyonLIP-IMAG, URA CNRS n∘ 1398Lyon Cedex 07France

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