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Relating Branching Program Size and Formula Size over the Full Binary Basis

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1563))

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Abstract

Circuit size, branching program size, and formula size of Boolean functions, denoted by C(f), BP(f), and L(f), are the most important complexity measures for Boolean functions. Often also the formula size L*(f) over the restricted basis {∨, ∧, ⌝} is considered. It is well-known that C(f) ≤ 3 BP(f), BP(f) ≤ L*(f), L*(f) ≤ L(f) 2, and C(f) ≤ L(f) - 1. These estimates are optimal. But the inequality BP(f) ≤ L(f) 2 can be improved to BP(f) ≤ 1.360 L(f) β, where β = log4(3 + √5) < 1.195.

The first and second author have been supported by DFG grant We 1066/8-1.

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Author information

Authors and Affiliations

  1. FB Informatik, LS 2, Univ. Dortmund, 44221, Dortmund, Germany

    Martin Sauerhoff & Ingo Wegener

  2. Frankfurt, Germany

    Ralph Werchner

Authors
  1. Martin Sauerhoff
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  2. Ingo Wegener
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  3. Ralph Werchner
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Editor information

Editors and Affiliations

  1. FB IV - Informatik, Universität Trier, D-54286, Trier, Germany

    Christoph Meinel

  2. LIFL, Université de Lille I, Bătiment 3, F-59655, Villeneuve d’Ascq Cedex, France

    Sophie Tison

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© 1999 Springer-Verlag Berlin Heidelberg

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Sauerhoff, M., Wegener, I., Werchner, R. (1999). Relating Branching Program Size and Formula Size over the Full Binary Basis. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_5

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  • DOI: https://doi.org/10.1007/3-540-49116-3_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65691-3

  • Online ISBN: 978-3-540-49116-3

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