Minimization or minimal DFS which means if you constructed a DFA on your own you might not get the same answer wish I got, but we get some DFA’s because some experience. Now the question is can we take any DFA and prove that or the DFA can be minimized, so that is called minimization of DFA

1. W E L C O M E T O O U R
P R E S E N TAT I O N

2. Our presentation topic is:
Equivalence and minimization of
DFA.

3. MINIMIZATION OF DFA.
• Minimization or minimal DFS which means if you constructed a DFA on
your own you might not get the same answer wish I got, but we get
some DFA’s because some experience. Now the question is can we take
any DFA and prove that or the DFA can be minimized, so that is called
minimization of DFA

4. WHAT IS THE BENEFIT OF MINIMIZING A
DFA?
• The principal reason to minimize a finite automation is to save the implementation
cost. When DFA were being studied, it was with respect to the machines that
implemented the function being studied. When an inverter or gate or memory
component consisted of one or more vacuum tubes, devices that cost money,
consumed power and took up considerable space, you really wanted to reduce the
number of tubes and the connections between them.
• Even with the move to solid state implementations, real estate was often a concern. If a
particular DFA automation was reused frequently in a system, optimizing the DFA paid
big dividends in chip yields.

5. DFA DIAGRAM AND TABLE
A
G H
B C D
FE
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0 1
A B F
B G C
C A C
D C G
E H F
F C G
G G E
H G C

6. DFA DIAGRAM
A
G H
B C D
FE
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0

7. TABLE FILLING ALGORITHM
0 1
A B F
B G C
C A C
D C G
E H F
F C G
G G E
H G C
A
B
C
D
E
F
G
H
X
X
X
XX X
X
X
X
X
X
X
X
X
X
A B C D E F G H
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X X
X X

8. 1 0 1 0
FC AB BG F AE BH
FG AD BC FE AG BG
F AE BH C BH G
FG AF BC FE EG HG
FE AG BG G DF C
FC AH BG
First Round: Second Round:

9. MINIMIZATION OF FINAL DFA.
A,E
G D,F
B,H C
1
0
0
0
1
1
0
1
0
0

10. THANK YOU.