Identify indistinguishable state in following state table and obtain minimized state diagram

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written 9.5 years ago by

teamques10 ★ 70k

Present,State	X = 0	-	X = 1	-
-	NS	O/P	NS	O/P
A	A	0	A	0
B	A	1	F	1
C	D	0	E	0
D	A	1	G	0
E	B	0	C	0
F	D	0	D	0
G	B	0	C	0

Equivalent states are identified and merged to reduce the number of states by using the method of partitioning.
First partition consists of all the states. $P_1$ = (A, B, C, D, E, F, G)
Second partition is done by observing outputs for each state and separating dissimilar output states. $P_2$ = (A, C, E, F, G) (B, D)
All the further partitions are done by separating states on the basis of their respective next states.
$P_3$ = (A)(C, E, F, G) (B, D)

$P_4$ = (A)(C, E, G) (F)(B)(D)

$P_5$ = (A)(C)(E,G) (F)(B)(D)
No further partitions are possible.
The states in the same partition are indistinguishable. These redundant states can be merged to reduce the number of states. Thus, E = G

Unique states are (A,B,C,D,E,F).
Reduced state table is:

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