Derandomizing Logspace With a Small Shared Hard Drive
Name
37_2025_Article_275.pdf
Size
440.71 KB
Format
Adobe PDF
Checksum (MD5)
a982b4899cecfea0a93ccd99ddb9bf24
Author(s)
Pyne, Edward
Date Issued
September 22, 2025
Journal
computational complexity
Publisher
Springer International Publishing
Citation
Pyne, E. Derandomizing Logspace With a Small Shared Hard Drive. comput. complex. 34, 13 (2025).
Version
Final published version
Abstract
We obtain new catalytic algorithms for space-bounded derandomization. In the catalytic computation model introduced by (Buhrman, Cleve, Koucký, Loff, and Speelman STOC 2013), we are given a small worktape, 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. We prove that B P S P A C E [ S ] ⊆ C S P A C E [ S , S 2 ] where B P S P A C E [ S ] corresponds to randomized space S computation, and C S P A C E [ S , C ] corresponds to catalytic algorithms that use O(S) bits of workspace and O(C) bits of catalytic space. Previously, only B P S P A C E [ S ] ⊆ C S P A C E [ S , 2 O ( S ) ] was known. In fact, we prove a general tradeoff, that for every α ∈ [ 1 , 1.5 ] , B P S P A C E [ S ] ⊆ C S P A C E [ S α , S 3 - α ] . We do not use the algebraic techniques of prior work on catalytic computation. Instead, we develop an algorithm that branches based on if the catalytic tape is conditionally random, and instantiate this primitive in a recursive framework. Our result gives an alternate proof of the best known time-space tradeoff for B P S P A C E [ S ] , due to (Cai, Chakaravarthy, and van Melkebeek, Theory Comput. Sys. 2006). As a final application, we extend our results to solve search problems in C S P A C E [ S , S 2 ] . As far as we are aware, this constitutes the first study of search problems in the catalytic computing model.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00037-025-00275-6
