Preliminaries
The following sets are finite languages over the binary alphabet {0, 1}.
∅ The empty set
{∈}: A language consisting only of one string of length 0
{00, 11, 0101}: A language containing three strings
A regular expression is a convenient means for compact representa-
tion of sets of strings. For example, the regular expression (01)* denotes
the set of strings that consists of the empty string, the string 01, and all
strings obtained by concatenating the string 01 with itself one or more
times. Note that (01)* denotes an infinite set. A formal definition of reg-
ular expressions follows:
Regular expression
Given a finite alphabet X, the following are regular expressions over X:
r
If a belongs to X,thena is a regular expression that denotes the
set ...