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International Conference on Fundamentals of Computation Theory

FCT 1985: Fundamentals of Computation Theory pp 494–502Cite as

The critical complexity of all (monotone) boolean functions and monotone graph properties

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 199))

Abstract

CREW-PRAM's build a powerful model of parallel computers. Cook/Dwork/Reischuk proved that the CREW-PRAM complexity of Boolean functions is bounded below by logbc(f) where b ≈ 4.79 and c(f) is the critical complexity of f. This lower bound is often even tight. For a class of functions F the critical complexity c(F), the minimum of all c(f) where f ∈ F, is the best general lower bound on the critical complexity of all f ∈ F. We determine the critical complexity of the set of all nondegenerate Boolean functions and all monotone nondegenerate Boolean functions up to a small additive term. And we compute exactly the critical complexity of the class of all monotone graph properties proving partially a conjecture of Turán.

Supported in part by DFG-grant No. We 1066/1-1

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References

  1. Cook,S.A./Dwork,C.: Bounds on the time for parallel RAM's to compute simple functions, 14. Symp. on Theory of Computing, 231–233, 1982

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  2. Cook,S.A./Dwork,C./Reischuk,R.: Upper and lower time bounds for parallel random access machines without simultaneous writes, to appear: SIAM Journal on Computing

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  3. Simon, H.U.: A tight Ω (loglog n)-bound on the time for parallel RAM's to compute nondegenerate Boolean functions, Symp. on Foundations of Computing Theory, Lect. Notes in Computer Science 158, 439–444, 1983

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  4. Turán, G.: The critical complexity of graph properties, Information Processing Letters 18, 151–153, 1984

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Authors and Affiliations

  1. FB 20-Informatik, Johann Wolfgang Goethe-Universität, 6000, Frankfurt a.M., Fed.Rep. of Germany

    Ingo Wegener

Authors
  1. Ingo Wegener
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Lothar Budach

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© 1985 Springer-Verlag Berlin Heidelberg

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Wegener, I. (1985). The critical complexity of all (monotone) boolean functions and monotone graph properties. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1985. Lecture Notes in Computer Science, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028833

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  • DOI: https://doi.org/10.1007/BFb0028833

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15689-5

  • Online ISBN: 978-3-540-39636-9

  • eBook Packages: Springer Book Archive

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