The Zeta Function of a Periodic-Finite-Type Shift
Akiko Manada, Navin Kashyap
TL;DR
This paper derives an efficient formula for computing the zeta function of periodic-finite-type shifts, a class of sofic shifts that extends shifts of finite type, facilitating analysis of their periodic sequences.
Contribution
The paper introduces a new, more efficient formula for the zeta function of PFTs, improving computational methods for analyzing their periodic structure.
Findings
The new formula simplifies the calculation of the zeta function for PFTs.
The formula is more efficient than existing methods for generic sofic shifts.
It enables better analysis of periodic sequences in PFTs.
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
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Taxonomy
TopicsCellular Automata and Applications · Mathematical Dynamics and Fractals · Quasicrystal Structures and Properties