CSE460 : Lecture 15 : State Identification; Homing ...

CSE460 : Lecture 15 : 1
State Identification;
Homing, Synchronizing, &
Distinguishing Sequences

Washington University
Spring 2006

http://www.arl.wustl.edu/~lockwood/class/cse460/

Copyright 2006, John W Lockwood

CSE460 : Lockwood

State Identification

• Consider some machine, M

• Probe the system Present Next Next
State state/ state/
– Apply Inputs Output Output
– Observe Output with X=0 with X=1
– Determine
A C/0 D/1
• Initial State
• Final State B C/0 A/1

• Example: C A/1 B/0

– Apply: 01 D B/0 C/1
– Apply: 011
2
CSE460 : Lockwood

State Uncertainties 3

• States

– S1 .. Sn

• Input

– Ii

• Successor

– Resulting States after input

• Eg: 1-successor: Resulting state(s) after input of “1”

• Uncertainty Vector

– (S1..Sk) (Sk+1..Sn) ..
– Homegeneous Vecor

• (Single State) or (Same states)

CSE460 : Lockwood

Successor Tree

S1 .. Sn
I1 Ip

(S1..Sk) (Sk+1..Sm) Present Next Next
I1 Ip State state/ state/
Output Output
• Result is homogeneous if with X=0 with X=1
Uncertainty vector contains
single state A C/0 D/1

B C/0 A/1

C A/1 B/0

D B/0 C/1

CSE460 : Lockwood 4

Homing Sequence

• Input Sequence = Homing Sequence

– Final state can be determine by response to input

• Uncertainty Vector Present Next Next
State state/ state/
– (S1..Sk) (Sk+1..Sm) .. Output Output
with X=0 with X=1
• (Components)
A B/0 D/0
• Terminate On
B A/0 B/0
– Homogeneous Vector
– Uncertainly appears earlier C D/1 A/0

• Example: D D/1 C/0

CSE460 : Lockwood 5

Example 2

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Example 2 - Continued

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Example 2 - Continued

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Synchronizing Sequence

• Takes machine to a specified state independent

of initial state or output.

– Ignores output

– Ignores requested state

– Terminate when: Present Next Next
state/
• Uncertainty seen earlier State state/ Output
with X=1
• Uncertainly contains one state Output
with X=0

A B/0 D/0

• Example: B A/0 B/0
C D/1 A/0

D D/1 C/0

CSE460 : Lockwood 9

Distinguishing Sequence

• Identifies Initial State

• Input Sequence = Present Next Next
Distinguishing State state/ state/
Sequence if Output Output
with X=0 with X=1
– Output is unique for
each possible initial A C/0 D/1
state
B C/0 A/1

C A/1 B/0

D B/0 C/1

CSE460 : Lockwood 10