### Periodic Decomposition of Sequential MachinesPeriodic Decomposition of Sequential Machines

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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