This talk will begin with a brief overview behind the theory of words in mathematics as well as the theory of finite automata in theoretical computer science. After this, we will define what an automatic sequence is, prove some fundamental theorems about them, and investigate some of their more intriguing properties. The majority of information presented comes from the text “Automatic Sequences: Theory, Applications, Generalisations” by Jean-Paul Allouche and the University of Waterloo's own Jeffrey Shallit, from the department of Computer Science.

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