Question
Asked Oct 14, 2019
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1. For the finite automaton below, find a minimal-state finite automaton
accepting the same language.
0
b
d
h
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1. For the finite automaton below, find a minimal-state finite automaton accepting the same language. 0 b d h

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Expert Answer

Step 1

Draw the table showing state transitions on different inputs:

States
Inputs
0
1
b
f
a
b
C
C
a
C
d
c
f
e
f
g
e
TO
h
C
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States Inputs 0 1 b f a b C C a C d c f e f g e TO h C

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Step 2

Now, reduce one of the two states which produce same outputs for both the inputs. States b and h are similar and states d and f are similar. Hence, states h and f can be removed. In place of h and f their equivalent states b and d can be mentioned. The reduced table will be:

States
Inputs
1
d
a
b
C
C
a
C
d
C
b
е
e
b0
bll
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States Inputs 1 d a b C C a C d C b е e b0 bll

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Step 3

Again, the states a and e are similar, so the state e can be removed. In place ...

States
Inputs
1
0
b
d
b
C
C
a
C
d
C
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States Inputs 1 0 b d b C C a C d C

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