Spring 10: CSci 4011—Formal Languages and Automata Theory
40 points
Homework 10
Out Fri., 4/16
Due Fri., 4/23
Please review the instructions given with Homework 1, as they apply to this home
work, too.
Please hand in your answers to the following.
Note:
All Exercise/Problem/Theorem/etc. numbers correspond to the
U.S. 2nd edition
of the
Sipser text. If you have the International edition, please check that the numbers match the ones in
the U.S. edition.
The presence of a hint in a problem does not necessarily mean that it is hard. It is merely to get
you started in the correct direction.
1.
Let
S
=
{a
M
A 
M
is a DFA and
M
accepts
w
R
whenever it accepts
w
}
. (Here
w
R
is the rever
sal of string
w
.) Prove that
S
is decidable.
Hint:
Use one of the deciders for regular languages from Sec. 4.1 as a subroutine in your decider
for
S
. You will also ±nd the result of Problem 6 in Homework 2 useful. (You may use this also as
a subroutine, without rewriting it.)
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 Spring '08
 NADATHUR
 Formal language, Regular expression, Automata theory, Languages and Automata Theory, CSci 4011—Formal Languages

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