On Poles of the Structure Generating Function of a Strongly Connected Automaton

Keisuke UCHIMURA

On Poles of the Structure Generating Function of a Strongly Connected Automaton

Keisuke UCHIMURA

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In this paper, we characterize the structure generating function of a strongly connected automaton. It is proved that poles of the minimal absolute value of the structure generating function are , e^2πi/h, , e^{2πi( h 1)/ h} where h is the period of a strongly connected automaton and r is the Frobenius's root of its incidence matrix. This result is a specialization of Berstol's result which characterizes the structure generating function in general. His method is based on the analysis. But we prove our results using some facts in linear algebra and graph theory. And we obtain analogous results for an automaton by considering the strongly connected automaton which contains as a subautomaton.

Publication: IEICE TRANSACTIONS on transactions Vol.E63-E No.4 pp.262-266

Publication Date: 1980/04/25

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Type of Manuscript: PAPER

Category: Automata and Languages

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Keisuke UCHIMURA

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Keisuke UCHIMURA, "On Poles of the Structure Generating Function of a Strongly Connected Automaton" in IEICE TRANSACTIONS on transactions, vol. E63-E, no. 4, pp. 262-266, April 1980, doi: .
Abstract: In this paper, we characterize the structure generating function of a strongly connected automaton. It is proved that poles of the minimal absolute value of the structure generating function are , e^2πi/h, , e^{2πi( h 1)/ h} where h is the period of a strongly connected automaton and r is the Frobenius's root of its incidence matrix. This result is a specialization of Berstol's result which characterizes the structure generating function in general. His method is based on the analysis. But we prove our results using some facts in linear algebra and graph theory. And we obtain analogous results for an automaton by considering the strongly connected automaton which contains as a subautomaton.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e63-e_4_262/_p

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@ARTICLE{e63-e_4_262,
author={Keisuke UCHIMURA, },
journal={IEICE TRANSACTIONS on transactions},
title={On Poles of the Structure Generating Function of a Strongly Connected Automaton},
year={1980},
volume={E63-E},
number={4},
pages={262-266},
abstract={In this paper, we characterize the structure generating function of a strongly connected automaton. It is proved that poles of the minimal absolute value of the structure generating function are , e^2πi/h, , e^{2πi( h 1)/ h} where h is the period of a strongly connected automaton and r is the Frobenius's root of its incidence matrix. This result is a specialization of Berstol's result which characterizes the structure generating function in general. His method is based on the analysis. But we prove our results using some facts in linear algebra and graph theory. And we obtain analogous results for an automaton by considering the strongly connected automaton which contains as a subautomaton.},
keywords={},
doi={},
ISSN={},
month={April},}

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TY - JOUR
TI - On Poles of the Structure Generating Function of a Strongly Connected Automaton
T2 - IEICE TRANSACTIONS on transactions
SP - 262
EP - 266
AU - Keisuke UCHIMURA
PY - 1980
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E63-E
IS - 4
JA - IEICE TRANSACTIONS on transactions
Y1 - April 1980
AB - In this paper, we characterize the structure generating function of a strongly connected automaton. It is proved that poles of the minimal absolute value of the structure generating function are , e^2πi/h, , e^{2πi( h 1)/ h} where h is the period of a strongly connected automaton and r is the Frobenius's root of its incidence matrix. This result is a specialization of Berstol's result which characterizes the structure generating function in general. His method is based on the analysis. But we prove our results using some facts in linear algebra and graph theory. And we obtain analogous results for an automaton by considering the strongly connected automaton which contains as a subautomaton.
ER -