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

  • Ingo Wegener
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 199)


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.


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  1. [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, 1982Google Scholar
  2. [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 ComputingGoogle Scholar
  3. [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, 1983Google Scholar
  4. [4]
    Turán, G.: The critical complexity of graph properties, Information Processing Letters 18, 151–153, 1984Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Ingo Wegener
    • 1
  1. 1.FB 20-InformatikJohann Wolfgang Goethe-UniversitätFrankfurt a.M.Fed.Rep. of Germany

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