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41 votes
41 votes

A finite state machine with the following state table has a single input $x$ and a single out $z$.

$$\begin{array}{|c|ll|}\hline
\textbf{present state} & \qquad \textbf{next state, z} \\ & \text{x=1}  & \text{x=0} \\\hline  \text{A} & \text{D,0} & \text{B,0} \\\hline   \text{B} & \text{B,1} & \text{C,1} \\\hline  \text{C} & \text{B,0} & \text{D,1}  \\\hline \text{D} & \text{B,1} & \text{C,0}  \\\hline \end{array}$$

If the initial state is unknown, then the shortest input sequence to reach the final state $C$ is:

  1. $01$
  2. $10$
  3. $101$
  4. $110$
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5 Answers

Best answer
62 votes
62 votes

 

  • if $A$ is start state , shortest sequence is $10$ or $00$ to reach $C$
  • if $B$ is start state , shortest sequence is $0$ to reach $C$
  • if $C$ is start state , shortest sequence is $10$ or $00$ to reach $C$
  • if $D$ is start state , shortest sequence is $0$ to reach $C$

B) is correct.

edited by
10 votes
10 votes

The answer should be zero O. But as options are given we can take string one by one and check, Option B "10" is matching. 

0 votes
0 votes
Acc. to me it should be B)
Answer:

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