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41st Annual Symposium on Foundations of Computer Science
Superlinear timespace tradeoff lower bounds for randomized computation
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
P. Beame, M. Saks, Xiaodong Sun, E. Vee, "Superlinear timespace tradeoff lower bounds for randomized computation," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 169, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892078, author = {P. Beame and M. Saks and Xiaodong Sun and E. Vee}, title = {Superlinear timespace tradeoff lower bounds for randomized computation}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {169}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892078}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Superlinear timespace tradeoff lower bounds for randomized computation SN  02725428 SP EP A1  P. Beame, A1  M. Saks, A1  Xiaodong Sun, A1  E. Vee, PY  2000 KW  randomised algorithms; computational complexity; probability; superlinear timespace tradeoff lower bounds; randomized computation; decision problems; deterministic RAM algorithms; deterministic Boolean branching programs; branching program; timespace tradeoff; lower bound VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
We prove the first timespace 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 timespace 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 timespace 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; superlinear timespace tradeoff lower bounds; randomized computation; decision problems; deterministic RAM algorithms; deterministic Boolean branching programs; branching program; timespace tradeoff; lower bound
Citation:
P. Beame, M. Saks, Xiaodong Sun, E. Vee, "Superlinear timespace tradeoff lower bounds for randomized computation," focs, pp.169, 41st Annual Symposium on Foundations of Computer Science, 2000
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