Characterization and topological behavior of homomorphism tree-shifts

The purpose of this article is twofold. On one hand, we reveal the equivalence shift finite type between a one-sided X and its associated hom tree-shift TX, as well in sofic shift. other investigate interrelationship among comparable mixing properties on tree-shifts those multidimensional spaces. They include irreducibility, topologically mixing, block gluing, strong all which are defined spirit classical shift, complete prefix code (CPC), uniform CPC. In summary, three manners coincide for TX. Furthermore, an irreducibility TA XA seen, so property XA, where space induced by matrix A tree-shift. These equivalences consistent with or when viewed degenerate