Note: On a zeta function associated with automata and codes

Authors:
Sylvain Lavallé/e;Christophe Reutenauer
Affiliations:
Université/ du Qué/bec Montré/al, Dé/pt. Mathé/matiques/ LACIM, C.P. 8888, Succ. A, QUE. H3C 3P8 Montré/al, Canada;Université/ du Qué/bec Montré/al, Dé/pt. Mathé/matiques/ LACIM, C.P. 8888, Succ. A, QUE. H3C 3P8 Montré/al, Canada
Venue:
Theoretical Computer Science
Year:
2007

Citing 6
Cited 0

Enumerative combinatorics

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Regular Article: N-Rationality of Zeta Functions

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Automata, Languages, and Machines

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Theory of Codes

Theory of Codes
Codes and aperiodic languages

1. Fachtagung über Automatentheorie und Formale Sprachen

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Abstract

The zeta function of a finite automaton A is exp{@?"n"="1^~a"nz^nn}, where a"n is the number of bi-infinite paths in A labelled by a bi-infinite word of period n. It reflects the properties of A: aperiodicity, nil-simplicity, existence of a zero. The results are applied to codes.