Opening Up the Distinguisher: A Hardness to Randomness Approach for BPL=L That Uses Properties of BPL
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3618260.3649772.pdf
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270.51 KB
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086928ef005cb1bd82f2a6dabdb5e128
Author(s)
Doron, Dean
Pyne, Edward
Tell, Roei
Date Issued
June 10, 2024
Publisher
ACM|Proceedings of the 56th Annual ACM Symposium on Theory of Computing
Citation
Doron, Dean, Pyne, Edward and Tell, Roei. 2024. "Opening Up the Distinguisher: A Hardness to Randomness Approach for BPL=L That Uses Properties of BPL."
Version
Final published version
Abstract
We provide compelling evidence for the potential of hardness-vs.-randomness approaches to make progress on the long-standing problem of derandomizing space-bounded computation. Our first contribution is a derandomization of bounded-space machines from hardness assumptions for classes of uniform deterministic algorithms, for which strong (but non-matching) lower bounds can be unconditionally proved. We prove one such result for showing that BPL=L “on average”, and another similar result for showing that BPSPACE[O(n)]=DSPACE[O(n)]. Next, we significantly improve the main results of prior works on hardness-vs.-randomness for logspace. As one of our results, we relax the assumptions needed for derandomization with minimal memory footprint (i.e., showing BPSPACE[S]⊆ DSPACE[c · S] for a small constant c), by completely eliminating a cryptographic assumption that was needed in prior work. A key contribution underlying all of our results is non-black-box use of the descriptions of space-bounded Turing machines, when proving hardness-to-randomness results. That is, the crucial point allowing us to prove our results is that we use properties that are specific to space-bounded machines.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial
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DOI of Published Version
https://doi.org/10.1145/3618260.3649772
