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## Paper 2: Regular Languages and Finite Automata

This Paper 2 course is taken by Part IA Computer Science Tripos students only.

Lecturer: Professor A.M. Pitts

No. of lectures: 6

This course is useful for Compiler Construction (Part IB) and Natural Language Processing (Part II).

Aims

The aim of this short course will be to introduce the mathematical formalisms of finite state machines, regular expressions and grammars, and to explain their applications to computer languages.

Lectures

• Regular expressions. Specifying sets of strings by pattern-matching.

• Finite state machines. Deterministic and non-deterministic finite automata and the languages they accept.

• Regular languages I. The language determined by a regular expression is regular.

• Regular languages II. Every regular language is determined by some regular expression.

• The Pumping Lemma. Proof and applications.

• Grammars. Context-free and regular grammars. The class of regular languages coincides with the class of languages generated by a regular grammar.

Objectives

At the end of the course students should

• be able to explain how to convert between the three ways of representing regular sets of strings introduced in the course; and be able to carry out such conversions by hand for simple cases

• be able to prove whether or not a given set of strings is regular

* Hopcroft, J.E., Motwani, R. & Ullman, J.D. (2001). Introduction to automata theory, languages, and computation. Addison-Wesley (2nd ed.).
Kozen, D.C. (1997). Automata and computability. Springer-Verlag.
Sudkamp, T.A. (2005). Languages and machines. Addison-Wesley (3rd ed.).

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