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COT 3100 Homework # 6 Solutions
Fall 2000
1)
Give regular expressions for each of the following languages: (Note: each language is
over the alphabet L = {a,b}
a)
The language of all strings containing the substring ab.
(a
∪
b)*ab(a
∪
b)*
b)
The language of all strings of length
≥
3.
(a
∪
b) (a
∪
b) (a
∪
b) (a
∪
b)*
c)
The language of all strings with exactly 3 b’s.
a*ba*ba*ba*
d)
The set of all strings where every
a is followed by 3 or more b’s.
b*(abbbb*)*
2)
Create a DFA to recognize the following languages over the alphabet L = {a,b}.
In each of these solns, the start state will be q0. Each final state will be
underlined. A self loop will be designated by the letter right above or below the
appropriate state.
a)
The language of all strings of odd length.
a,b
q0 > q1
<
a,b
b)
The language of all strings that contain exactly 2n a’s where n is an integer.
b
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 Fall '09

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