On the parallel evaluation of classes of circuits

  • S. Rao Kosaraju
Invited Paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 472)


We treat the problem of parallel evaluation of two important classes of circuits: polynomial degree circuits, and leveled monotone planar circuits. We show that if the operators form a non-commutative semi-ring, then there exists a circuit of degree 0(n) and size 0(n) for which the minimum depth after any restructuring is n. We also establish that any leveled monotone planar boolean circuit of size n can be evaluated by poly(n) processors in 0(log3n) parallel time.


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  1. 1.
    P. W. Dymond, and S. A. Cook: Hardware Complexity and Parallel Computation, Proceedings of the 21st Annual Symp. on Foundations of Computer Science, 1980, 360–372.Google Scholar
  2. 2.
    L. M. Goldschlager: A Space Efficient Algorithm for the Monotone Planar Circuit Value Problem, IPL, 1980, 25–27.Google Scholar
  3. 3.
    L. M. Goldschlager, and I. Parberry: On the Construction of Parallel Computers from Various Bases of Boolean Functions, Theoretical Computer Science, 1986, 43–58.Google Scholar
  4. 4.
    R. E. Ladner: The Circuit Value Problem is log space complete for P, SIGACT News 7, 1975, 18–20.Google Scholar
  5. 5.
    G. L. Miller, V. Ramachandran, and E. Kaltofen: Efficient Parallel Evaluation of Straight-line Code and Arithmetic Circuits, Lecture Notes in Computer Science 227, VLSI Algorithms and Architectures, 1986, 236–245.Google Scholar
  6. 6.
    L. G. Valiant, S. Skyum, S. Berkowitz, and C. Rackoff: Fast Parallel Computation of Polynomials Using Few Processors, SIAM J. on Computing, 1983, 641–644.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • S. Rao Kosaraju
    • 1
  1. 1.Department of Computer ScienceThe Johns Hopkins UniversityBaltimore

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