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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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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