Student Working Seminar in Groups and Dynamics

Date: October 25, 2017

Time: 1:00PM - 2:00PM

Location: BLOC 628

Speaker: Roman Kogan

Title: Finite-state automata and measures

Abstract: The idea of self-similarity has been prominently used in group theory ever since the introduction of the Grigorchuk group, generated by states of a finite-state machine with output, to answer Milnor's question on intermediate growth of groups. Similar ideas can be applied to the study of measures on the space of sequences in a finite alphabet to define finite-state measures. These measures generalize Bernoulli, Markov and k-step Markov measures in a natural way, and are preserved by the action of invertible finite-state automorphisms. We introduce and briefly discuss the properties of these measures, such as when they are k-step Markov, and when their image under non-invertible automorphisms is finite-state.