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International Workshop on Computer Science Logic

CSL 1987: CSL '87 pp 138–150Cite as

The conjunctive complexity of quadratic boolean functions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 329))

Abstract

The minimal number of conjunctions in monotone circuits for quadratic Boolean functions, i.e. disjunctions of quadratic monomials xi xj, is investigated. Single level circuits which have only one level of conjunctions are compared with arbitrary monotone circuits. The computation of the single level complexity is shown to be NP complete. For almost all quadratic functions almost optimal circuits can be computed in polynomial time. The single level conjecture is disproved, i.e. some quadratic function is defined whose single level complexity is larger than its conjunctive complexity.

Supported in part by DFG grants No. We 1066/1-2 and Me 872/1-1

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Authors and Affiliations

  1. Lehrstuhl für Theoretische Informatik II, Universität Dortmund, 4600, Dortmund 50, Fed. Rep. of Germany

    Katja Lenz & Ingo Wegener

Authors
  1. Katja Lenz
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  2. Ingo Wegener
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Egon Börger Hans Kleine Büning Michael M. Richter

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© 1988 Springer-Verlag

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Lenz, K., Wegener, I. (1988). The conjunctive complexity of quadratic boolean functions. In: Börger, E., Büning, H.K., Richter, M.M. (eds) CSL '87. CSL 1987. Lecture Notes in Computer Science, vol 329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50241-6_35

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  • DOI: https://doi.org/10.1007/3-540-50241-6_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50241-8

  • Online ISBN: 978-3-540-45960-6

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