Colleges and Schoolshttp://hdl.handle.net/1969.1/28152018-07-15T23:01:24Z2018-07-15T23:01:24ZMeasures Induced by Automata and Their Actionshttp://hdl.handle.net/1969.1/1667072018-07-06T13:14:12Z2017-12-14T00:00:00ZMeasures Induced by Automata and Their Actions
In this thesis we explore the theme of automata, measures on spaces of sequences X^N
in a finite alphabet X, and their connections. The notion of a finite-state measure (a measure
given by a finite automaton, or equivalently, having a finite number of sections) is introduced,
and applied to the problem of studying the images of Markov measures under the
action of tree automorphisms given by automata. Another approach, based on prior work
by Kravchenko, is also applied to this problem to compute the Radon-Nikodym derivative
in the case when the automaton has polynomial growth, and to compute frequencies by
using a lift to (S x X)^N.
The question of when the image of a finite-state measure under the action of a noninvertible
automaton is answered. We also explore when a finite-state measure is Gibbs.
For the second part of the thesis, we introduce the notion of the automatic logarithm,
and a measure associated with it. We compute this measure for certain interesting examples,
in which it turns out to be finite-state.
2017-12-14T00:00:00ZPeer Review of Teaching Pre-Observation Formhttp://hdl.handle.net/1969.1/1666912018-06-22T12:52:12Z2018-06-22T00:00:00ZPeer Review of Teaching Pre-Observation Form
2018-06-22T00:00:00ZPeer Review of Teaching Post-Observation Reflection Formhttp://hdl.handle.net/1969.1/1666902018-06-22T12:45:46Z2018-06-22T00:00:00ZPeer Review of Teaching Post-Observation Reflection Form
2018-06-22T00:00:00ZPeer Review of Teaching Observation Noteshttp://hdl.handle.net/1969.1/1666892018-06-22T11:26:43Z2018-06-22T00:00:00ZPeer Review of Teaching Observation Notes
2018-06-22T00:00:00Z