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Fast parallel algorithms for finding all prime implicants for discrete functions

  • Section VI: Complexity Of Boolean Functions
  • Conference paper
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Logic and Machines: Decision Problems and Complexity (LaM 1983)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 171))

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Abstract

We consider the problem of enumerating the prime implicants of a given discrete function as a basic task of circuit theory. First, we count PI's for random Boolean functions. Then we use the well known lattice differentiation as a tool for finding implicants. The concept of a peak admits to characterize prime implicants, at least those with no improper domains. The improper case can be reduced to a lower dimensional problem. Since the peak test is local, a parallel algorithm is available. The time and space complexity turns out to be low measured in the input size.

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Authors and Affiliations

  1. Lehrstuhl für Angewandte Mathematik, insbesondere Informatik, RWTH Aachen, 5100, Aachen, Germany

    W. Oberschelp

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  1. W. Oberschelp
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Editor information

E. Börger G. Hasenjaeger D. Rödding

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© 1984 Springer-Verlag Berlin Heidelberg

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Oberschelp, W. (1984). Fast parallel algorithms for finding all prime implicants for discrete functions. In: Börger, E., Hasenjaeger, G., Rödding, D. (eds) Logic and Machines: Decision Problems and Complexity. LaM 1983. Lecture Notes in Computer Science, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13331-3_56

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  • DOI: https://doi.org/10.1007/3-540-13331-3_56

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13331-5

  • Online ISBN: 978-3-540-38856-2

  • eBook Packages: Springer Book Archive

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