Introduction to Symbolic Dynamics

Content

This is a cycle of seminars on the first five chapters of the book An Introduction to Symbolic Dynamics and Coding by Douglas Lind and Brian Marcus.

I meant it as a way of learning something by teaching it to others.

Issues

1. First talk: April 7, 2010
   • Introduction
   • Shift spaces
   • Basic constructions on shift spaces
   • Sliding block codes
   • A parallel with coding theory
2. Second talk: April 14, 2010
   • Shifts of finite type
   • Graphs and their shifts
   • Graphs as presentations of shifts
   • An application to data recording
3. Third talk: April 28, 2010
   • State splitting
   • Sofic shifts
   • Characterization of sofic shifts
   • Minimal right-resolving presentation
4. Fourth talk: May 12, 2010
   • Constructions on sofic shifts
   • Entropy of a shift space
   • Computing entropy via Perron-Frobenius theory
5. Fifth talk: May 19, 2010
   • Cyclic structure of irreducible matrices
   • Road-colorings and right-closing labelings
   • The finite-state coding theorem

Last update: May 19, 2010