Simulating Time with Square-Root Space
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3717823.3718225.pdf
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738.01 KB
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Adobe PDF
Checksum (MD5)
6fad3d12cefa22af24cbcb625183bbef
Author(s)
Williams, R. Ryan
Date Issued
June 15, 2025
Publisher
ACM|Proceedings of the 57th Annual ACM Symposium on Theory of Computing
Citation
R. Ryan Williams. 2025. Simulating Time with Square-Root Space. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC '25). Association for Computing Machinery, New York, NY, USA, 13–23.
Version
Final published version
Abstract
We show that for all functions t(n) ≥ n, every multitape Turing machine running in time t can be simulated in space only O(√t logt). This is a substantial improvement over Hopcroft, Paul, and Valiant’s simulation of time t in O(t/logt) space from 50 years ago [FOCS 1975, JACM 1977]. Among other results, our simulation implies that bounded fan-in circuits of size s can be evaluated on any input in only √s · poly(logs) space, and that there are explicit problems solvable in O(n) space which require at least n2−ε time on every multitape Turing machine for all ε > 0, thereby making a little progress on the P versus PSPACE problem.
Our simulation reduces the problem of simulating time-bounded multitape Turing machines to a series of implicitly-defined Tree Evaluation instances with nice parameters, leveraging the remarkable space-efficient algorithm for Tree Evaluation recently found by Cook and Mertz [STOC 2024].
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
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3717823.3718225
