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CS381
First Mid Term Solutions
Fall 2005
1.
Let
( )
1
1
1
01
1
, ,
,
,
M
Q
q F
δ
=
Σ
and
( )
2
2
2
02
2
, ,
,
,
M
Q
q
F
=
Σ
be finite automata.
Construct a finite automaton M that accepts the language
( ) ( )
1
1
2
2
L M
L M
I
.
( )
1
2
1
2
, , ,
M
Q Q
F F
=
×
Σ
×
where
[ ]
( ) ( ) ( )
,
,
,
,
,
q p a
q a
p a
=
2.
Write a regular expression denoting the set of all strings of 0’s
and 1’s such that every 1 is immediately preceded by at least two
consecutive 0’s.
Suggestion:
To make sure your answer is correct ask your self
some simple questions such as does your expression work for
strings with an even number of 1’s, an odd number of 1’s, short
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 Fall '05
 HOPCROFT

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