Sharvari Tikekar
TIFR, Mumbai
November 24, 2022
Shifts of finite type associated to an integer matrix: Shifts of finite type are one of the fundamental objects in the field of symbolic dynamics. These are the spaces of one-sided or two-sided sequences over a finite set of symbols where certain finitely many words are "forbidden". The shift spaces exhibit a natural association with $0-1$ matrices. In this talk we will first discuss some necessary preliminaries related to the one-sided shifts of finite type associated to a non-negative integer matrix. Words which correspond to the matrix entries greater than $1$ are thought to have multiplicity and thus are called "repeated words". Now, for any given collection $mathcal{F}$ of forbidden words and $mathcal{R}$ of repeated words, we define two notions: multiplicity of a word and generalized language. We define the shift determined by $mathcal{F}$ and $mathcal{R}$, and obtain necessary and sufficient conditions for when the language of this shift is precisely the generalized language. Finally, we compute the entropy of this shift using the g
TIFR, Mumbai
November 24, 2022
Shifts of finite type associated to an integer matrix: Shifts of finite type are one of the fundamental objects in the field of symbolic dynamics. These are the spaces of one-sided or two-sided sequences over a finite set of symbols where certain finitely many words are "forbidden". The shift spaces exhibit a natural association with $0-1$ matrices. In this talk we will first discuss some necessary preliminaries related to the one-sided shifts of finite type associated to a non-negative integer matrix. Words which correspond to the matrix entries greater than $1$ are thought to have multiplicity and thus are called "repeated words". Now, for any given collection $mathcal{F}$ of forbidden words and $mathcal{R}$ of repeated words, we define two notions: multiplicity of a word and generalized language. We define the shift determined by $mathcal{F}$ and $mathcal{R}$, and obtain necessary and sufficient conditions for when the language of this shift is precisely the generalized language. Finally, we compute the entropy of this shift using the g