The Boolean functions computed by random Boolean formulas or how to grow the right function

Authors

  • Alex Brodsky,

    Corresponding author
    1. Department of Computer Science, University of Toronto, Toronto, Ontario, M5S 3G4, Canada
    • Department of Computer Science, University of Toronto, Toronto, Ontario, M5S 3G4, Canada
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    • Supported by an NSERC PGS B and a Killam Predoctoral Fellowship.

  • Nicholas Pippenger

    1. Department of Computer Science, Princeton University, Princeton, New Jersey, 08544
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    • Supported by an NSERC Discovery Grant and a Canada Research Chair.


  • The research reported here was done while the authors were in the Department of Computer Science, University of British Columbia, Vancouver, BC, Canada.

Abstract

We characterize growth processes (probabilistic amplification) by their initial conditions to derive conditions under which results such as Valiant's J Algorithms 5 (1984), 363–366 hold. We completely characterize growth processes that use linear connectives and generalize Savický's Discrete Math 147 (1990), 95–103 analysis to characterize growth processes that use monotone connectives. Additionally, we obtain explicit bounds on the convergence rates of several growth processes, including the growth process studied in Savický. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005

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