Minimally Generated Subshifts

We introduce the notion of a minimal generator G for the coded system X; that is a generator for coded systemX whenever u ۲ G, then u ۶۲ W(< G n fug >). Such an X is called minimally generated system. We aim tointroduce a class of minimally generated systems generated by some certain synchronizing blocks. If an irreduciblesystem has at least one synchronizing block, then it is called a synchronized system. A version of a theorem of K.Thomsen (۲۰۰۶) in minimally generated systems has been given. The derived set has been characterized as well.