2010/10/27 by Paulette N. Willis, Willis, Paulette N.
Computer Science · Mathematics · #37B10 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Operator Algebras (math.OA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1010.5739
openalex publication_date 2010/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Exel and Renault proved that a sliding block code on a one-sided shift space coming from a progressive block map is a local homeomorphism. We provide a counterexample showing that the converse does not hold. We use this example to generalize the notion of progressive to a property of block maps we call weakly progressive, and we prove that a sliding block code coming from a weakly progressive block map is a local homeomorphism. We also introduce the notion of a regressive block map and prove that a sliding block code *-commutes with the shift map if and only if it comes from a regressive block map. We also prove that a sliding block code is a local homeomorphism and *-commutes with the shift map if and only if it is a k-fold covering map defined from a regressive block map.