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Finite Automata and Algebraicity of Formal Power Series over Finite Fields

This project is intended to study the relations of automatic sequences with algebra. To this end, we first look at stringology. We study finite-state automata and then automatic sequences that are produced by finite automata. Then to be able to prove two important results about the relation of automatic sequences and algebraicity of formal power series over finite fields, we study Cobham’s theorem which is known to be a very important theorem in automata theory. After these two important results, i.e. Christol’s theorem and Furstenberg’s theorem, we present a partial proof of a conjecture of Jason Bell. The material from sections 2, 3 and 4 of this project comes mostly from [2]. I also consulted [8] and [15] for a specific theorem and a specific example, respectively.