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The extended future cover of a sofic shift

Klaus Thomsen

Abstract

The paper describes a cover of the future cover of a sofic shift which is canonical in the same way as the future cover itself. In some cases the cover is isomorphic to the future cover and in other it is a genuine extension.

The extended future cover of a sofic shift

Abstract

The paper describes a cover of the future cover of a sofic shift which is canonical in the same way as the future cover itself. In some cases the cover is isomorphic to the future cover and in other it is a genuine extension.
Paper Structure (11 sections, 25 theorems, 80 equations)

This paper contains 11 sections, 25 theorems, 80 equations.

Table of Contents

  1. Introduction
  2. Terminology and notation
  3. Constructing the future cover
  4. On the merging of a labeled graph
  5. A cover of the future cover
  6. Strongly canonical covers of the future cover
  7. The main result
  8. Proof of the main result
  9. Recap of material from Th
  10. The non-wandering part
  11. Filling in the blanks

Key Result

Lemma 3.1

Assume that $(H,L_H)$ is right-resolving. Let $v,w \in V_{H}$. There is a labeled arrow $f_H(v) \overset{a}{\to} f_H(w)$ in $([H],L_{[H]})$ if and only if there is a labeled arrow $v \overset{a}{\to} u$ in $(H,L_H)$ such that $f_H(u) =f_H(w)$.

Theorems & Definitions (45)

  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Proposition 3.4
  • proof
  • Corollary 3.5
  • Lemma 3.6
  • ...and 35 more