Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
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
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)).
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
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