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Nearly optimal hierarchies for network and formula size

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Summary

How large are the “gaps” in the complexity hierarchies for Boolean functions with respect to network size and formula size? A gap is a non-empty interval of integers none of which is the complexity of any Boolean function. It is shown for the most natural bases that there are no gaps at all over a broad range of values and that the largest gap anywhere is less than n.

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Authors and Affiliations

  1. Department of Computer Science, University of Warwick, CV4 7AL, Coventry, UK

    M. S. Paterson

  2. FB20-Informatik, J.W. Goethe-Universität, D-6000, Frankfurt a.M, Federal Republic of Germany

    I. Wegener

Authors
  1. M. S. Paterson
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  2. I. Wegener
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Additional information

Supported in part by a Senior Fellowship of the SERC and by DFG grant No. We 1066/1-1

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Paterson, M.S., Wegener, I. Nearly optimal hierarchies for network and formula size. Acta Informatica 23, 217–221 (1986). https://doi.org/10.1007/BF00289499

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  • DOI: https://doi.org/10.1007/BF00289499

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