1. Homing sequence: to identify the final state.
The input sequence which, when applied starting in any initial state, allows the final state to be uniquely determined by observing the output sequence produced.
(A, B, C, D) 1
(C)
(A, D)
(A)
C/0 B/0 D/1 C/0 A/1 A/0 C/0 D/0
ABCD
I S
Input seq: 00 Output seq: 01 A Output seq: 10 C
All machine has homing sequence
Synchronizing sequence: the input sequence which drives a machine to a known state, independent of the output sequence produced.
(A, B, C, D) 1
(B, C, D)
(C, D)
(D)
A/1 B/0 B/0 C/0 C/0 D/0 D/1 D/1
ABCD
I S
111: synchronizing sequence

2. This machine does not have synchronizing sequence
A/0 B/0 B/1 D/0 C/1 A/0 C/0 A/1
ABCD
I S
(A, B, C, D) 1
(A, B, C)
(A, B, D)
This machine does not have synchronizing sequence