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Summary: Theory of Computation
Lecture 5: Regular Expressions
Max Alekseyev
University of South Carolina
January 24, 2012
Lecture Outline
Regular expressions
Regular Expressions and Regular Languages
Generalized NFA
Atomic Regular Expressions
Let be a fixed alphabet. A regular expression, or regexp for
short, is an expression that describes a particular language over .
If r is a regular expression, we write L(r) for the language
described by r. We may also just use the regexp itself in place of
the language it describes.
Primitive (atomic) regular expresions are:
describes the empty language L() = ;
describes the language L() = {} consisting of just the
empty string; and
a for a describes the language L(a) = {a} consisting of
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