Little explanation of state minimization through an example.

1. WELCOME
Daffodil International University
Subject: Theory of Computing
Benzir Ahmed
Speaker
Daffodil International University
Department :Computer Science and Engineering
Faculty :Science and Information Technology
Topic: State Minimization

2. State Minimization
Why : 1. Reduce number of latches
assign minimum-length encoding
only as the logarithm of the number
of states
2. Increase the number of unassigned states
codes
heuristic to improve state-assignment
and logic-optimization
Goal: Identify and remove redundant states
(states which can not be observed)
Let’s Get Start

3. 0
0 0
0
0
0
0
0
1
1 1
1
1
1
1
1
A B
E F
D
G H
C
Let’s Consider an Example-

4. The Process
Find out the accepting state.
Remove unreachable states.
Draw pairs
Combining unmarked state
0
0 0
0
0
0
0
0
1
1 1
1
1
1
1
1
A B
E F
D
G H
C

5. Drawing pairs
B
C
E
F
G
H
BA C E F G
0
0
0
0
0
0
0
1
1 1
1
1
1
1
A B
E F G H
C
A B C D E F G H
A B C D E F G H
ROW
COLUMN

6. Drawing pairs
B
C
E
F
G
H
BA C E F G
X₀ X₀
X₀
X₀
X₀
X₀
0
0
0
0
0
0
0
1
1 1
1
1
1
1
A B
E F G H
C
A B C D E F G H
A B C D E F G H
ROW
COLUMN

7. B
C
E
F
G
H
BA C E F G
X₀ X₀
X₀
X₀
X₀
X₀
0
0
0
0
0
0
0
1
1 1
1
1
1
1
A B
E F G H
C
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁ X ₁ B
B
0
1
G
C
A
A
0
1
B
F

8. B
C
E
F
G
H
BA C E F G
X₁
X₁
X₁
X₁
X₁
X₁
X₁
X₁
X₁ X₁
X₁
X₁
X₀ X₀
X₀
X₀
X₀
X₀
0
0
0
0
0
0
0
1
1 1
1
1
1
1
A B
E F G H
C
X₂
G
G
0
1
G
E
A
A
0
1
B
F

9. B
C
E
F
G
H
BA C E F G
X₀ X₀
X₀
X₀
X₀
X₀
0
0
0
0
0
0
1
1
1
1
1
B,H
F G
CA,E
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁
X ₁ X ₁
The Result
X₂

10. ANY
QUESTIONS?

11. THANKS FOR
WATCHING