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COT 3100 Homework # 5 Solutions
Spring 2000
1)
Give regular expressions for each of the following languages: (Note: each language is
over the alphabet L = {a,b}
Note: there are many other correct answers for each of these.
a)
The language of all strings containing at least one a and one b.
(aa*b U bb*a)(a U b)*
b)
The language of all strings of length
≥
2.
(a U b)(a U b)(a U b)*
c)
The language of all strings with exactly 4 a’s.
b*ab*ab*ab*ab*
d)
The set of all strings where contiguous letters are ALWAYS different.
(ab)*a U (ba)*b U (ab)* U (ba)*
2)
Create a DFA to recognize the following languages over the alphabet L = {a,b}.
a)
The language of all strings of even length.
Let your states be s1 and s2.
Let s1 be a start state.
Let s1 be the only final state.
Let both transitions from s1 go to s2, and
both transitions from s2 go to s1.
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The language of all strings that contain exactly 3n a’s where n is an integer.
Let your states be s1, s2, and s3.
Let s1 be the start state.
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 Spring '09

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