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CSC236: Homework 4
March 17, 2010
Question 1
Part (a)
The automaton accepts words over
{
a,b
}
*
where the number of
a
s is congurent
to the number of
b
s modulo 3.
Part (b)
A
B
C
Part (c)
Prove by induction that:
•
The new DFA is in state
A
i± the old DFA is in one of the states 1
,
5
,
9;
•
The new DFA is in state
B
i± the old DFA is in one of the states 2
,
6
,
7;
•
The new DFA is in state
C
i± the old DFA is in one of the states 3
,
4
,
8.
The induction base is true since the initial states are
A
and 1. The induction
step follows by considering all the possible transitions.
Finally, note that the new DFA accepts i± it is in state
A
, which happens
i± the old DFA is is one of the states 1
,
5
,
9, which happens i± the old DFA
accepts. Thus the two DFAs recognize the same language.
1
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View Full Document Question 2
Here is the DFA:
O
A
0
A
1
R
0
R
1
0
1
1
0
0
1
0
1
1
0
Here are the semantics of the di±erent states:
1. State
O
captures the empty string.
2. States
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This note was uploaded on 04/11/2010 for the course CSC CSC236 taught by Professor Farzanazadeh during the Spring '10 term at University of Toronto Toronto.
 Spring '10
 FarzanAzadeh

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