CS 452
Formal Languages and Automata Theory
Summer 2004
Midterm Problems
Problem 1.
(22 pts)
Consider the regular expression
α
= (
a
∗
ab
∗
b
)
∗
.
(a)
•
(2 pts)
Find strings
u
and
v
of length

u

=

v

= 7, such that
u
∈
L
(
α
) and
v /
∈
L
(
α
).
(b)
••
(10 pts)
Construct a
DFA
that accepts the language
L
(
α
) that is charac
terized by the regular expression
α
.
(c)
••
(10 pts)
Given some regular expression
R
, can you think of a method to
come up with a regular expression
R
′
, such that
L
(
R
′
) =
L
(
R
) ?
Use that method to build a regular expression
α
′
that characterizes the lan
guage
L
(
α
′
) =
L
(
α
) for the regular expression given above.
Problem 2.
(35 pts)
For each of the following languages decide whether it is a
regular or a context free language or neither. If it is regular or context free show
it by providing either a regular expression, a finite automaton (
DFA
or
NFA
, your
choice), a
PDA
, or a context free grammar that characterizes the language.
Use
each representation at least once.
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 Spring '08
 Deftel
 pts, Formal language, Regular expression

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