Minimally Generated Subshifts



We introduce the notion of a minimal generator G for the coded system X; that is a generator for coded system X whenever u 2 G, then u 62 W(< G n fug >). Such an X is called minimally generated system. We aim to introduce a class of minimally generated systems generated by some certain synchronizing blocks. If an irreducible system has at least one synchronizing block, then it is called a synchronized system. A version of a theorem of K. Thomsen (2006) in minimally generated systems has been given. The derived set has been characterized as well.