1
Question
Given the following state table of an FSM with two states A and B, one input and one output:
Present
State A
Present
State B
Input
Next
State A
Next
State B
Output
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
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If the initial state is A = 0, B = 0, what is the minimum length of an input string which will take the machine to the state A = 0, B = 1 with Output = 1?
| Present State A |
Present State B |
Input | Next State A |
Next State B |
Output |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 1 |
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Solution
The transition diagram for the given FSM is given below.
As can be seen from above diagram the minimum length of the input string that will take machine from 00 to 01 with output 1, is three.
In fact the minimum length input string is "101"
Which will give an output of 1, while reaching state 01.
As can be seen from above diagram the minimum length of the input string that will take machine from 00 to 01 with output 1, is three.
In fact the minimum length input string is "101"
Which will give an output of 1, while reaching state 01.
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