Semi-strongly irreducible shifts
This paper continues the author's study of local functions on subshifts. In earlier work [PU.M.A., Pure Math. Appl. 11, 471--484 (2000; Zbl 0980.37004)] the author showed the equivalence of pre-injectivity and surjectivity for irreducible shifts of finite type, then in [Theor. Comput. Sci. 299, 477--493 (2003; Zbl 1042.68077)] she defined a notion of strong irreducibility which together with a finite type condition ensures the same property for such shifts in \(A^{\Gamma}\), where \(\Gamma\) is an amenable group. Here, the work is taken in a slightly different direction, with the introduction of a property called semi-strong irreducibility, with the result that pre-injectivity implies surjectivity for a local function on a semi-strongly irreducible shift of finite type in \(A^{\Gamma}\) for any group \(\Gamma\) of non-exponential growth. An interesting byproduct is a proof that proper subshifts of such shifts have strictly smaller entropy.
scientific article; zbMATH DE number 2107246
scientific article