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Size-time complexity of Boolean networks for prefix computations

Authors:

F. P. PreparataAuthors Info & Claims

STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

Pages 436 - 442

https://doi.org/10.1145/28395.28442

Published: 01 January 1987 Publication History

Abstract

The prefix problem consists of computing all the products x₀x₁…x_j (j=0, …, N - 1), given a sequence x = (x₀, x₁, …, x_{N - 1}) of elements in a semigroup. In this paper we completely characterize the size-time complexity of computing prefixes with boolean networks, which are synchronized interconnections of Boolean gates and one-bit storage devices. This complexity crucially depends upon a property of the underlying semigroup, which we call cycle-freedom (no cycle of length greater than one in the Cayley graph of the semigroup). Denoting by S and T size and computation time, respectively, we have S = Θ((N/T) log(N/T)), for non-cycle-free semigroups, and S = Θ(N/T), for cycle-free semigroups. In both cases, T ∈ [Ω(logN), O(N)].

References

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Cited By

Becker BSparmann U(1989)Computations over finite monoids and their test complexity[1989] The Nineteenth International Symposium on Fault-Tolerant Computing. Digest of Papers10.1109/FTCS.1989.105583(299-306)Online publication date: 1989
https://doi.org/10.1109/FTCS.1989.105583
Aggarwal AChandra ARaghavan PSimon J(1988)Energy consumption in VLSI circuitsProceedings of the twentieth annual ACM symposium on Theory of computing10.1145/62212.62230(205-216)Online publication date: 1-Jan-1988
https://dl.acm.org/doi/10.1145/62212.62230

Index Terms

Size-time complexity of Boolean networks for prefix computations
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Network flows
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows
  2. Randomness, geometry and discrete structures

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cover image ACM Conferences

STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

January 1987

471 pages

ISBN:0897912217

DOI:10.1145/28395

Editor:
Alfred V. Aho

Copyright © 1987 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 January 1987

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Cited By

Becker BSparmann U(1989)Computations over finite monoids and their test complexity[1989] The Nineteenth International Symposium on Fault-Tolerant Computing. Digest of Papers10.1109/FTCS.1989.105583(299-306)Online publication date: 1989
https://doi.org/10.1109/FTCS.1989.105583
Aggarwal AChandra ARaghavan PSimon J(1988)Energy consumption in VLSI circuitsProceedings of the twentieth annual ACM symposium on Theory of computing10.1145/62212.62230(205-216)Online publication date: 1-Jan-1988
https://dl.acm.org/doi/10.1145/62212.62230

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