Claude Elwood Shannon

Pyotr Sergeyevich Novikov

Metamathematics II, MATH 503, CRN 29992, Spring 2010

Instructor: Christian Rosendal, room 416 SEO

Course hours and location: Monday - Wednesday - Friday, 10:00-10:50 AM. Taft Hall 321.

Office hours: By appointment in my office SEO 416.

Talks on additional topics: Course description:
The course will be an introduction to the theory of computation with a particular emphasis on formal languages and finite automata. Thus, instead of studying the wider class of partial recursive functions and corresponding recursive sets, we shall concentrate on regular languages and, if time permits, their infinite analogs. The theory of finite automata is of interest in linguistics, theoretical computer science and has found new and interesting applications in geometric and combinatorial group theory. We shall present a number of applications to group theory, including the study of normal forms in finitely generated groups and the word problem.

Tentative course plan Literature:
There is no required text for the course since the lectures will be based on multiple sources. However, for the material on regular languages and finite state automata, a number of textbooks are available. Since the basic theory is well-established, most books on basic automata will contain the equivalence of regular languages and languages recognised by finite state automata, the closure properties of regular languages, non-deterministic finite automata and the Myhill-Nerode Theorem.

Some suggested books:
Lecture notes: Decidability results using automata on infinite words and trees: Homework: I will assign a number of homework exercises in the course of the semester most of which I will try to go through in class.

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