Relating branching program size and formula size over the full binary basis

Authors:
Martin Sauerhoff;Ingo Wegener;Ralph Werchner
Affiliations:
FB Informatik, Univ. Dortmund, Dortmund, Germany;FB Informatik, Univ. Dortmund, Dortmund, Germany;Frankfurt, Germany
Venue:
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Year:
1999

Citing 5
Cited 0

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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) ≤ 3BP(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)