Manouchehr Shahamat - Department of Mathematics, Dezful branch, Islamic Azad University, Dezful, Iran

‎‎Synchronized systems‎, ‎has attracted much attention in ۱۹۸۶ by F. Blanchard and G. Hansel, and extension of them has been of interest since that notion was introduced in ۱۹۹۲ 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_{-۱}x_{۰}m and mv any block in X one has again \ldots x_{-۱}x_{۰}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 ۰\leq \ell\leq \infty‎.‎‎ ‎‎‎To do this we consider a \beta-shift and will replace ۱ with some blocks u_i‎ ‎to have countable many new systems‎. ‎Then‎, ‎we will merge them‎.‎

‎minimal half synchronizing‎, ‎synchronizing, Entropy