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The number of states in the minimal deterministic finite automaton corresponding to the regular expression (0 + 1)*(10) is ____________
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    5
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The number of states in the minimal deterministic finite automaton cor...
Below is NFA for the given regular expression (0 + 1)*(10)
Below is DFA for the same. 
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Most Upvoted Answer
The number of states in the minimal deterministic finite automaton cor...
To understand why the minimal deterministic finite automaton (DFA) corresponding to the regular expression (0 1)*(10) has 3 states, we need to break down the regular expression and construct the DFA step by step.

Regular expression breakdown:
(0 1)*: This part allows any number of occurrences of either 0 or 1.
10: This part requires the sequence "10" to appear.

Constructing the DFA:

1. Start state (S0):
- At the start state, any input of 0 or 1 is accepted, and the automaton remains in the start state.
- Transition: S0 --(0,1)--> S0

2. Intermediate state (S1):
- After reading the first "1", the automaton moves to an intermediate state to check for the occurrence of "10".
- Transition: S0 --1--> S1

3. Final state (S2):
- If the next input is "0", the automaton moves to the final state, accepting the regular expression.
- Transition: S1 --0--> S2

4. Dead state (S3):
- If any input other than "0" is encountered after being in the intermediate state (S1), the automaton moves to a dead state, indicating that the regular expression is not matched.
- Transition: S1 --1--> S3

The resulting DFA:

0,1
+---------+
| |
V |
S0 --(0,1)--> S0
| |
| |
V |
S1 --1--> S2 |
| |
| |
V |
S3 --1--> S3 |
+---------+

Number of states in the DFA: 3
- The DFA consists of three states: S0, S1, and S2.
- S0 is the start state, S2 is the final state, and S1 is an intermediate state.
- S3 is a dead state, which is not counted as part of the minimal DFA.

Therefore, the correct answer is option 'B' (3).
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The number of states in the minimal deterministic finite automaton corresponding to the regular expression (0 + 1)*(10) is ____________a)2b)3c)4d)5Correct answer is option 'B'. Can you explain this answer?
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