Manada, Akiko and Kashyap, Navin (2013) On the zeta function of a periodic-finite-type shift. In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E96A (6). pp. 1024-1031.
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Abstract
Periodic-finite-type shifts (PFT's) are sofic shifts which forbid the appearance of finitely many pre-specified words in a periodic manner. The class of PFT's strictly includes the class of shifts of finite type (SFT's). The zeta function of a PET is a generating function for the number of periodic sequences in the shift. For a general sofic shift, there exists a formula, attributed to Manning and Bowen, which computes the zeta function of the shift from certain auxiliary graphs constructed from a presentation of the shift. In this paper, we derive an interesting alternative formula computable from certain ``word-based graphs'' constructed from the periodically-forbidden word description of the PET. The advantages of our formula over the Manning-Bowen formula are discussed.
| Item Type: | Journal Article |
|---|---|
| Publication: | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
| Publisher: | Institute of Electronics, Information and Communication Engineers |
| Additional Information: | Copyright of this article belongs to Institute of Electronics, Information and Communication Engineers. |
| Keywords: | Periodic-Finite-Type Shift; Zeta Function; Word-Based Graph; Möbius Inversion Formula |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 19 Jul 2013 07:19 |
| Last Modified: | 19 Jul 2013 07:19 |
| URI: | http://eprints.iisc.ac.in/id/eprint/46855 |
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