Abstract
Nisan [6] showed that any randomized logarithmic space algorithm (running in polynomial time and with two-sided error) can be simulated by a deterministic algorithm that runs simultaneously in polynomial time and Θ(log2 n) space. Subsequently Saks and Zhou [9] improved the space complexity and showed that a deterministic simulation can be carried out in space Θ(log1.5 n). However, their simulation runs in time \(n^{\Theta({\rm log}^{0.5} n)}\). We prove a time-space tradeoff that interpolates these two simulations. Specifically, we prove that, for any 0≤ α ≤ 0.5, any randomized logarithmic space algorithm (running in polynomial time and with two-sided error) can be simulated deterministically in time \(n^{O(log^{0.5-\alpha}n)}\) and space O(log 1.5 + α n). That is, we prove that BPL ⊆ DTISP[\(n^{O(log^{0.5-\alpha}n)}\), O(log 1.5 + α n)].
A more detailed version of the paper is available at http://www.cs.wisc.edu/ dieter. Research supported in part by NSF grants CCR-9634665, CCR-0208013 and CCR-0133693.
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© 2004 Springer-Verlag Berlin Heidelberg
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Cai, JY., Chakaravarthy, V.T., van Melkebeek, D. (2004). Time-Space Tradeoff in Derandomizing Probabilistic Logspace. In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_50
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DOI: https://doi.org/10.1007/978-3-540-24749-4_50
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