The Structure of Catalytic Space: Capturing Randomness and Time via Compression
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3717823.3718112.pdf
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790.93 KB
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Author(s)
Cook, James
Li, Jiatu
Mertz, Ian
Pyne, Edward
Date Issued
June 15, 2025
Publisher
ACM|Proceedings of the 57th Annual ACM Symposium on Theory of Computing
Citation
James Cook, Jiatu Li, Ian Mertz, and Edward Pyne. 2025. The Structure of Catalytic Space: Capturing Randomness and Time via Compression. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC '25). Association for Computing Machinery, New York, NY, USA, 554–564.
Version
Final published version
Abstract
In the catalytic logspace (CL) model of (Buhrman et. al. STOC 2013), we are given a small work tape, and a larger catalytic tape that has an arbitrary initial configuration. We may edit this tape, but it must be exactly restored to its initial configuration at the completion of the computation. This model is of interest from a complexity-theoretic perspective as it gains surprising power over traditional space. However, many fundamental structural questions remain open.
We substantially advance the understanding of the structure of CL, addressing several questions raised in prior work. Our main results are as follows.
1: We unconditionally derandomize catalytic logspace: CBPL = CL.
2: We show time and catalytic space bounds can be achieved separately if and only if they can be achieved simultaneously: any problem in both CL and P can be solved in polynomial time-bounded CL.
3: We characterize deterministic catalytic space by the intersection of randomness and time: CL is equivalent to polytime-bounded, zero-error randomized CL.
Our results center around the compress--or--random framework.
For the second result, we introduce a simple yet novel compress--or--compute algorithm which, for any catalytic tape, either compresses the tape or quickly and successfully computes the function at hand. For our first result, we further introduce a compress--or--compress--or--random algorithm that combines runtime compression with a second compress--or--random algorithm, building on recent work on distinguish-to-predict transformations and pseudorandom generators with small-space deterministic reconstruction.
Description
STOC ’25, Prague, Czechia
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivatives
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DOI of Published Version
https://doi.org/10.1145/3717823.3718112
