NDLI: Super-linear time-space tradeoff lower bounds for randomized computation

Content Provider	IEEE Xplore Digital Library
Author	Beame, P. Saks, M. Xiaodong Sun Vee, E.
Copyright Year	2000
Description	Author affiliation: Dept. of Comput. Sci. & Eng., Washington Univ., Seattle, WA, USA (Beame, P.)
Abstract	We prove the first time-space lower bound tradeoffs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are an extension of those used by M. Ajtai (1999) in his time-space tradeoffs for deterministic RAM algorithms computing element distinctness and for deterministic Boolean branching programs computing an explicit function based on quadratic forms over GF(2). Our results also give a quantitative improvement over those given by Ajtai. Ajtai shows, for certain specific functions, that any branching program using space S=o(n) requires time T that is superlinear. The functional form of the superlinear bound is not given in his paper, but optimizing the parameters in his arguments gives T= /spl Omega/(n log log n/log log log n) for S=0(n/sup 1-/spl epsiv//). For the same functions considered by Ajtai, we prove a time-space tradeoff of the form T=/spl Omega/(n/spl radic/(log(n/S)/log log(n/S))). In particular for space 0(n/sup 1-/spl epsiv//), this improves the lower bound on time to /spl Omega/(n/spl radic/(log n/log log n)).
Starting Page	169
Ending Page	179
File Size	1116578
Page Count	11
File Format	PDF
ISBN	0769508502
ISSN	02725428
DOI	10.1109/SFCS.2000.892078
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2000-11-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Binary decision diagrams Computer science Mathematics Complexity theory Sorting Computer errors Read-write memory History Turing machines Input variables
Content Type	Text
Resource Type	Article

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