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Redondo Beach, California

Nov. 12, 2000 to Nov. 14, 2000

ISBN: 0-7695-0850-2

pp: 169

M. Saks , Dept. of Comput. Sci. & Eng., Washington Univ., Seattle, WA, USA

P. Beame , Dept. of Comput. Sci. & Eng., Washington Univ., Seattle, WA, USA

E. Vee , Dept. of Comput. Sci. & Eng., Washington Univ., Seattle, WA, USA

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)).

INDEX TERMS

randomised algorithms; computational complexity; probability; super-linear time-space tradeoff lower bounds; randomized computation; decision problems; deterministic RAM algorithms; deterministic Boolean branching programs; branching program; time-space tradeoff; lower bound

CITATION

M. Saks,
P. Beame,
E. Vee,
"Super-linear time-space tradeoff lower bounds for randomized computation",

*FOCS*, 2000, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2000, pp. 169, doi:10.1109/SFCS.2000.892078