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Author Hennie, F. C. ♦ Stearns, R. E.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1966
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract It has long been known that increasing the number of tapes used by a Turing machine does not provide the ability to compute any new functions. On the other hand, the use of extra tapes does make it possible to speed up the computation of certain functions. It is known that a square factor is sometimes required for a one-tape machine to behave as a two-tape machine and that a square factor is always sufficient.The purpose of this paper is to show that, if a given function requires computation time $\textit{T}$ for a $\textit{k}-tape$ realization, then it requires at most computation time $\textit{T}$ log $\textit{T}$ for a two-tape realization. The proof of this fact is constructive; given any $\textit{k}-tape$ machine, it is shown how to design an equivalent two-tape machine that operates within the stated time bounds. In addition to being interesting in its own right, the trade-off relation between number of tapes and speed of computation can be used in a diagonalization argument to show that if $\textit{T}(\textit{n})$ and $\textit{U}(\textit{n})$ are two time functions such that inf $\textit{T}(\textit{n})$ log $\textit{T}(\textit{n})$ ÷ $\textit{U}(\textit{n})$ = 0 then there exists a function that can be computed within the time bound $\textit{U}(\textit{n})$ but not within the time bound $\textit{T}(\textit{n}).$
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1966-10-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 13
Issue Number 4
Page Count 14
Starting Page 533
Ending Page 546

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Source: ACM Digital Library