1
Department of Mathematics, Dezful branch, Islamic Azad University, Dezful, Iran.
2
Department of Mathematics, Quchan University of Technology, Quchan, Iran.
10.22080/cjms.2023.25757.1664
Abstract
We introduce the notion of a minimal generator $G$ for the coded system $X$; that is a generator for coded system $X$ whenever $u \in G$, then $u \not \in W(\overline{})$. Such an $X$ is called \emph{minimally generated system}. We aim to introduce a class of minimally generated subshifts generated by some certain synchronizing blocks. These systems are precisely the tool that will enable us to show that for such subshifts $X$, each $x \in X$ can be written uniquely as $x=\ldots v_{-1}v_{0}v_1v_2\ldots$, where $\{\ldots ,v_{-1},v_{0},v_1,v_2,\ldots\}\in G$. Shows that the converse of that proposition isn't necessarily true. {\color{red} We will show which of the components of the Kreiger graph of such a subshift could be a candidate to be suitable for a Fischer cover. }
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