NDLI: A Note on Bennetts Time-Space Tradeoff for Reversible Computation

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Sherman, Alan T. Levine, Robert Y.
Copyright Year	1990
Abstract	Given any irreversible program with running time T and space complexity S, and given any $\varepsilon > 0$, Bennett shows how to construct an equivalent reversible program with running time $O(T^{1+\varepsilon })$ and space complexity $O(S \ln T)$. Although these loose upper bounds are formally correct, they are misleading due to a hidden constant factor in the space bound. It is shown that this constant factor is approximately $\varepsilon 2^{1 / \varepsilon}$, which diverges exponentially as $\varepsilon$ approaches 0. Bennetts analysis is simplified using recurrence equations and it is proven that the reversible program actually runs in time $\Theta ({{T^{1 + \varepsilon}} / {S^{\varepsilon}}})$ and space $\Theta (S(1+\ln ({T / S})))$.Bennett claims that for any $\varepsilon > 0$, the reversible program can be made to run in time $O(T)$ and space $O(ST^{\varepsilon })$. This claim is corrected and tightened as follows: whenever $T \geqq 2S$ and for any $\varepsilon \geqq {1 / {(0.58 \lg ({T / S}))}}$, the reversible program can be made to run in time $\Theta (T)$ and space $\Omega (S(T/S)^{\varepsilon/2})\cap O(S(T/S)^\varepsilon )$. For $S\leqq T < 2S$, Bennetts 1973 simulation yields an equivalent reversible program that runs in time $\Theta (T)$ and space $\Theta (S)$.
Starting Page	673
Ending Page	677
Page Count	5
File Format	PDF
ISSN	00975397
DOI	10.1137/0219046
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	19
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	Models of computation algorithms reversible computation time-space tradeoff Complexity classes
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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