Question

The above figure shows what is called a finite state machine. The machine reads one word at a time and transitions to a new state. The states are indicated by boxes and the transitions by arrows. There are three states S0, S1 and S2 and the last is the final state (indicated by two coincident boxes). The text beside each arrow means the following: DT = determiner (a, an, the), AJ = adjective, NN = noun. The machine starts at S0 and on seeing a determiner (DT) enters the state S1. Then if it sees an adjective (AJ), it remains in the same state. But at state S1 if it sees a noun (NN), it enters the final state. The final state is also called the “accept” state. No other states or state transitions are defined or permitted. 
Which of the following will cause the machine to enter S2, the accept state? 

• A. The blue sky
• B. A vast blue sky
• C. The sky
• D. A very blue sky

Hint:

Finite state machines accept only those inputs that exactly match their defined transitions; any undefined category causes rejection.

Answer 1

The Correct Option is A, B, C

To determine which sequence of words will cause the finite state machine to enter the final state S2, we need to analyze how the machine transitions between its states.

The states and transitions are defined as follows:

• The machine starts at S0.
• From S0, on seeing a determiner (DT), it transitions to S1.
• At S1, if it sees an adjective (AJ), it remains in S1.
• At S1, if it sees a noun (NN), it transitions to the final state S2 (accept state).

Now, let's analyze each option:

1. The blue sky:
   - "The" is a determiner (DT) leading to state S1.
   - "Blue" is an adjective (AJ), remaining in S1.
   - "Sky" is a noun (NN), transitioning to S2.
   This sequence leads to the accept state S2.
2. A vast blue sky:
   - "A" is a determiner (DT) leading to state S1.
   - "Vast" and "blue" are adjectives (AJ), staying in S1.
   - "Sky" is a noun (NN), transitioning to S2.
   This sequence also leads to the accept state S2.
3. The sky:
   - "The" is a determiner (DT) leading to state S1.
   - "Sky" is a noun (NN), transitioning to S2.
   This sequence leads directly to the accept state S2.
4. A very blue sky:
   - "A" is a determiner (DT) leading to state S1.
   - "Very" and "blue" are adjectives (AJ), remaining in S1.
   - "Sky" is a noun (NN), transitioning to S2.
   This sequence also leads to the accept state S2.

Therefore, the sequences "The blue sky," "A vast blue sky," "The sky," and "A very blue sky" all lead the machine to enter the accept state S2.