NDLI: On the complexity of integer multiplication in branching programs with multiple tests and in read-once branching programs with limited nondeterminism

Content Provider	IEEE Xplore Digital Library
Author	Woelfel, P.
Copyright Year	2002
Description	Author affiliation: FB Informatik, Dortmund Univ., Germany (Woelfel, P.)
Abstract	Branching programs (BPs) are a well-established computation and representation model for Boolean functions. Although exponential lower bounds for restricted BPs such as read-once branching programs (BP1s) have been known for a long time, the proof of lower bounds for important selected functions is sometimes difficult. Especially the complexity of fundamental functions such as integer multiplication in different BP models is interesting. In (Bolling and Woelfel, 2001), the first strongly exponential lower bound of /spl Omega/(2/sup n/4/) has been proven for the complexity of integer multiplication in the deterministic BP1 model. Here, we consider two well-studied BP models which generalize BP1s by allowing a limited amount of nondeterminism and multiple variable tests, respectively. More precisely, we prove a lower bound of /spl Omega/(2/sup n/(7k)/) for the complexity of integer multiplication in the (V, k)-BP model. As a corollary, we obtain that integer multiplication cannot be represented in polynomial size by nondeterministic BP1s, if the number of nondeterministic nodes is bounded by log n - log log n - /spl omega/ (1). Furthermore, we show that any (1, +k)-BP representing integer multiplication has a size of /spl Omega/(2[n/48(k+1)]). This is not polynomial for k = o(n/log n).
Sponsorship	IEEE Comput. Soc. Tech. Committee on Math. Found. Comput. (TCMF) SIGACT EATCS Centre de Recherches Math., Univ. Montreal Math. Inf. Technol. & Complex Syst. (MITACS)
Starting Page	80
Ending Page	89
File Size	378655
Page Count	10
File Format	PDF
ISBN	0769514685
ISSN	10930159
DOI	10.1109/CCC.2002.1004343
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-05-21
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Binary decision diagrams Testing Boolean functions Computational modeling Polynomials Data structures Turing machines Computational complexity
Content Type	Text
Resource Type	Article

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