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Author Bal, Marie-Pierre ♦ Perrin, Dominique
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2003
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Generating sequences ♦ Rational sequences ♦ Regular languages ♦ Regular sequences
Abstract The main result is a characterization of the generating sequences of the length of words in a regular language on $\textit{k}$ symbols. We say that a sequence $\textit{s}$ of integers is regular if there is a finite graph $\textit{G}$ with two vertices i, t such that $s_{n}$ is the number of paths of length $\textit{n}$ from $\textit{i}$ to $\textit{t}$ in $\textit{G}.$ Thus the generating sequence of a regular language is regular. We prove that a sequence $\textit{s}$ is the generating sequence of a regular language on $\textit{k}$ symbols if and only if both sequences $\textit{s}$ = $(s_{n})_{n≥0}$ and $\textit{t}$ = $(k^{n}$ ™ $s_{n})_{n≥0}$ are regular.
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 2003-11-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 50
Issue Number 6
Page Count 26
Starting Page 955
Ending Page 980

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Source: ACM Digital Library