The zeta function of a periodic-finite-type shift

Authors:
Akiko Manada;Navin Kashyap
Affiliations:
Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada;Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Year:
2009

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Abstract

The class of periodic-finite-type shifts (PFT's) is a class of sofic shifts that strictly includes the class of shifts of finite type (SFT's), and the zeta function of a PFT is a generating function for the number of periodic sequences in the shift. In this paper, we derive a useful formula for the zeta function of a PFT. This formula allows the zeta function of a PFT to be computed more efficiently than the specialization of a formula known for a generic sofic shift.