On images of sofic systems

Abstract

Let $\Sigma$ and $\bar{\Sigma }$ be finite alphabets. For topologically transitive sofic systems $X\subset {\Sigma }^{\mathbb{Z}}$ and $\tilde{X}\subset {\tilde{\Sigma }}^{\mathbb{Z}}$ we give a necessary and sufficient condition for the existence of a homomorphism from $X$ to $\tilde{X}$. For topologically mixing sofic systems $X\subset {\Sigma }^{\mathbb{Z}}$ and $\tilde{X}\subset {\tilde{\Sigma }}^{\mathbb{Z}}$, such that the topological entropy of $\tilde{X}$ is less than the topological entropy of $X$, we give a necessary and sufficient condition for the existence of a homomorphism of $X$ onto $\tilde{X}$.

21 pages

Cited by in corpus (2)

• Category Theory of Symbolic Dynamics
• Universality in symbolic dynamics constrained by Medvedev degrees