CSE 105: Automata and Computability Theory
Winter 2011
Homework #5
Due: Tuesday, March 1st, 2011
Problem 1
Let
COMPL
DFA
be the language
h
A, B
i
A
and
B
are DFAs over the same alphabet Σ and
L
(
A
) =
L
(
B
)
.
(Notice the complementation bar over
L
(
B
) above!) Show that
COMPL
DFA
is decid
able.
Problem 2
We say that a string over the alphabet Σ =
{
0
,
1
}
is
sorted
if any 0s in it occur
before any 1s. (For example, 111 is sorted, whereas 00110 is not.) We consider the
empty string to be sorted. Let
MESSY
DFA
be the language
n
h
A
i
A
is a DFA over the alphabet Σ =
{
0
,
1
}
and no string in
L
(
A
) is sorted
o
.
Show that
MESSY
DFA
is decidable.
Hint:
Think about intersecting two regular languages.
Problem 3
(Sipser 4.22) A
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 Spring '99
 Paturi
 Regular expression, Automata theory, Pushdown automaton

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