COT 4210 (Proof) Homework #1: Regular Languages
Due Date: Thursday September 8, 2011
Note: Unless otherwise noted, assume the alphabet for each language is {0, 1}.
1) Draw the state diagram for the DFA formally described below:
{Q, Σ, δ, q
0
, F} where
Q = {q
0
, q
1
, q
2
, q
3
, q
4
}
Σ = {0, 1}
Start state = q
0
F = {q
1
, q
3
}
δ =
0
1
q
0
q
0
q
1
q
1
q
4
q
0
q
2
q
3
q
4
q
3
q
0
q
1
q
4
q
2
q
3
2) Draw a DFA that accepts the following language:
{ w  w’s decimal equivalent is divisible by 6 }
3) Draw a DFA that accepts the following language: { w  w starts with 11 or ends with 00 }
4) Draw an NFA that accepts the following language:
{ w  w contains either the substring 1101 or 0110 }
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View Full Document5) Prove that every NFA can be converted to another equivalent NFA that has only one accept
state.
6) Your friend Tommy thinks that if he swaps the accept and reject states in an NFA that accepts
a language L, that the resulting NFA must accept the language
L
. Show, by way of counter
example, that Tommy is incorrect. Explain why your counterexample is one.
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 Spring '08
 Staff
 Regular expression, Regular language, Nondeterministic finite state machine

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