Title of article :
INFINITE MINIMAL HALF SYNCHRONIZING
Author/Authors :
Shahamat ، Manouchehr Department of Mathematics - Islamic Azad University, Dezful branch
From page :
105
To page :
113
Abstract :
‎‎Synchronized systems‎, ‎has attracted much attention in 1986 by F. Blanchard and G. Hansel, and extension of them has been of interest since that notion was introduced in 1992 by D. Fiebig and U. Fiebig. ‎One was via half synchronized systems; that is‎, ‎systems having half synchronizing blocks‎. ‎In fact‎, ‎if for a left transitive ray such as $\ldots x_{-1}x_{0}m$ and $mv$ any block in $X$ one has again $\ldots x_{-1}x_{0}mv$ a left ray in $X$‎, ‎then $m$ is called half synchronizing. ‎A block $m$ is minimal (half-)synchronizing, ‎whenever $w \varsubsetneq m$‎, ‎$w$ is not (half-)synchronizing‎. ‎Examples with $\ell$ minimal (half-)synchronizing blocks has been given for $0\leq \ell\leq \infty$‎.‎‎ ‎‎‎To do this we consider a $\beta$-shift and will replace 1 with some blocks $u_i$‎ ‎to have countable many new systems‎. ‎Then‎, ‎we will merge them‎.‎
Keywords :
Minimal half synchronizing , Synchronizing , Entropy
Journal title :
Journal of Mahani Mathematical Research Center
Journal title :
Journal of Mahani Mathematical Research Center
Record number :
2743839
Link To Document :
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