### Structural Theory of Transition Classes

Mahsa Allahbakhshi

Abstract.
Given a finite-to-one factor code $\pi$ from a one dimensional shift of
finite type $X$ onto a sofic shift $Y$ there is a well-known quantity
assigned to $\pi$ called the degree of the code and is defined to be the
minimal number of preimages of points of $Y$. When $\pi:X\to Y$ is
infinite-to-one, a notion analogous to the degree of a finite-to-one code,
called the class degree, was defined recently. The class degree is the
minimal number of transition equivalence classes over points of $Y$ where
the definition of transition classes is motivated by communicating classes
in Markov chains. We show that the class degree is in fact a generalization
of the degree and satisfies similar properties.
Joint work with S. Hong and U. Jung.