Extracting invariants of conjugacy from independence entropy

Abstract

The concept of independence entropy for symbolic dynamical systems was introduced in Louidor et al. [Independence entropy of Zd-shift spaces, Acta Appl. Math. 126 (2013), pp. 297–317]. This notion of entropy measures the extent to which one can freely insert symbols in positions without violating the constraints defined by the shift space. Independence entropy is not invariant under topological conjugacy. We define an invariant version of the independence entropy by setting This invariant is bounded above by the topological entropy. We prove that equality holds for all sofic shift spaces over then we give an example showing that equality does not hold for general shift spaces.