Exponent trajectories in symbolic dynamics

Symbolic dynamics

This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results on embeddings of shifts of finite type. The second one is the connection between syntactic semigroups and the classification of sofic shifts up to conjugacy.

Symbolic Representation of Trajectories for Skill Generation

The completion of robot programs requires long development time and much e~ort. To shorten this programming time and minimize the e~ort, we have been developing a system which we refer to as "assemblyplan-from-observation (APO) system;" this system provides the ability for a robot to observe a human performing an assembly task, understand the task, and subsequently generate a program to perform...

Complex Dynamics and Symbolic Dynamics

Robert L. Devaney, Boston University Synopsis As so often happens in mathematics, there is a surprising connection between two quite distinct subfields of dynamical systems theory, namely the structure of the automorphism group of the one sided shift map on d-symbols and the topology of the analogue of the Mandelbrot set for degree d polynomials of one complex variable. In this lecture we will ...

Forbidden Words in Symbolic Dynamics

We introduce an equivalence relation between functions from to . By describing a symbolic dynamical system in terms of forbidden words, we prove that the -equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the system. We show that the new invariant is independent from previous ones, but it is not characteristic. In the case of sof...

Open Problems in Symbolic Dynamics