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2011 26th Annual IEEE Conference on Computational Complexity
Making Branching Programs Oblivious Requires Superlogarithmic Overhead
San Jose, California USA
June 08June 11
ISBN: 9780769544113
ASCII Text  x  
Paul Beame, Widad Machmouchi, "Making Branching Programs Oblivious Requires Superlogarithmic Overhead," 2012 IEEE 27th Conference on Computational Complexity, pp. 1222, 2011 26th Annual IEEE Conference on Computational Complexity, 2011.  
BibTex  x  
@article{ 10.1109/CCC.2011.35, author = {Paul Beame and Widad Machmouchi}, title = {Making Branching Programs Oblivious Requires Superlogarithmic Overhead}, journal ={2012 IEEE 27th Conference on Computational Complexity}, volume = {0}, year = {2011}, issn = {10930159}, pages = {1222}, doi = {http://doi.ieeecomputersociety.org/10.1109/CCC.2011.35}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2012 IEEE 27th Conference on Computational Complexity TI  Making Branching Programs Oblivious Requires Superlogarithmic Overhead SN  10930159 SP12 EP22 A1  Paul Beame, A1  Widad Machmouchi, PY  2011 KW  timespace tradeoffs KW  lower bounds KW  branching programs KW  oblivious computation KW  randomization VL  0 JA  2012 IEEE 27th Conference on Computational Complexity ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2011.35
We prove a timespace tradeoff lower bound of $T =\Omega\left(n\log(\frac{n}{S}) \log \log(\frac{n}{S})\right) $ forrandomized oblivious branching programs to compute $1GAP$, alsoknown as the pointer jumping problem, a problem for which there is asimple deterministic time $n$ and space $O(\log n)$ RAM (randomaccess machine) algorithm.%Although no simulations of general%computation on randomized oblivious algorithms requiring only%polylogarithmic increase in time and space are yet known, our lower%bound implies that a superlogarithmic factor increase in time and%space is in fact necessary in any such simulation.We give a similar timespace tradeoff of $T =\Omega\left(n\log(\frac{n}{S}) \log \log(\frac{n}{S})\right)$ forBoolean randomized oblivious branching programs computing$GIP$$MAP$, a variation of the generalized inner product problem thatcan be computed in time $n$ and space $O(\log^2 n)$ by adeterministic Boolean branching program.These are also the first lower bounds for randomized obliviousbranching programs computing explicit functions that apply for$T=\omega(n\log n)$. They also show that any simulation ofgeneral branching programs by randomized oblivious ones requires eithera superlogarithmic increase in time or an exponential increase in space.
Index Terms:
timespace tradeoffs, lower bounds, branching programs, oblivious computation, randomization
Citation:
Paul Beame, Widad Machmouchi, "Making Branching Programs Oblivious Requires Superlogarithmic Overhead," ccc, pp.1222, 2011 26th Annual IEEE Conference on Computational Complexity, 2011
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