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2011 IEEE 26th Annual Conference on Computational Complexity (2011)
San Jose, California USA
June 8, 2011 to June 11, 2011
ISSN: 1093-0159
ISBN: 978-0-7695-4411-3
pp: 12-22
We prove a time-space 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 time-space 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.
time-space tradeoffs, lower bounds, branching programs, oblivious computation, randomization

P. Beame and W. Machmouchi, "Making Branching Programs Oblivious Requires Superlogarithmic Overhead," 2011 IEEE 26th Annual Conference on Computational Complexity(CCC), San Jose, California USA, 2011, pp. 12-22.
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