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Author Gill, Arthur ♦ Flexer, J. Robert
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1967
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract Given a minimal sequential machine $\textit{M}$ and a positive integer $\textit{T},$ it is desired to partition the state set of $\textit{M}$ into $\textit{T}$ classes, say $\textit{S}0,$ $\textit{S}1,$ · · ·, $\textit{S}\textit{T}-1,$ such that all states in $\textit{S}1,$ under all possible inputs, pass into states in $\textit{S}\textit{i}+1$ (mod $\textit{T}).$ If such a $\textit{T}-partition$ exists, $\textit{M}$ can be realized by means of periodically-varying logic, which often results in the saving of memory elements. The period of $\textit{M}$ is defined as the greatest common divisor of all cycle lengths of $\textit{M}—a$ quantity which can be readily evaluated since it depends only on a finite set of independent loops exhibited by the state graph.The main result is that a $\textit{T}-partition$ exists for $\textit{M}$ if and only if $\textit{T}$ is a divisor of the period of $\textit{M}.$ For every such $\textit{T},$ an algorithm is given for constructing the corresponding partition. If $\textit{M}$ is not required to be minimal, it is shown (constructively) that a $\textit{T}-partition$ exists for every $\textit{T}.$
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 1967-10-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 14
Issue Number 4
Page Count 11
Starting Page 666
Ending Page 676

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Source: ACM Digital Library