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Consider the language L given by the regular expression (a + b) *b(a +b) over the alphabet {a, b}. The smallest number of states needed in a deterministic finite-state automaton (DFA) accepting L is ______.
Note: This questions appeared as Numerical Answer Type.
Note: This questions appeared as Numerical Answer Type.
- a)3
- b)4
- c)5
- d)6
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the language L given by the regular expression (a + b) *b(a +...
NFA to DFA Conversion:
In the STT below you can see 4 states are there but before confirming the ans lets try to minimize, It cant be minimized further because A goes to Nonfinal Nonfinal & AB goes to Final Final hence can not be merged. Similarly ∗AC goes NF NF & ∗ABC goes to F F hence can not be merged. Hence, 4 is the final answer.
Most Upvoted Answer
Consider the language L given by the regular expression (a + b) *b(a +...
Solution:
The given regular expression is (a b)*b(a b).
We need to find the smallest number of states needed in a DFA accepting L.
We can construct a DFA for L as follows:
1. Start with an initial state q0.
2. For each input symbol a, create a transition from q0 to a new state q1, labeled with a.
3. For each input symbol b, create a transition from q0 to q2, labeled with b.
4. For each input symbol a, create a transition from q1 to q2, labeled with a.
5. For each input symbol b, create a transition from q1 to q3, labeled with b.
6. For each input symbol a, create a transition from q2 to q1, labeled with a.
7. For each input symbol b, create a transition from q2 to q2, labeled with b.
8. For each input symbol a, create a transition from q3 to q2, labeled with a.
9. For each input symbol b, create a transition from q3 to q3, labeled with b.
10. Mark q3 as the final state.
The DFA constructed above has 4 states.
Therefore, the smallest number of states needed in a DFA accepting L is 4.
Hence, option B is the correct answer.
The given regular expression is (a b)*b(a b).
We need to find the smallest number of states needed in a DFA accepting L.
We can construct a DFA for L as follows:
1. Start with an initial state q0.
2. For each input symbol a, create a transition from q0 to a new state q1, labeled with a.
3. For each input symbol b, create a transition from q0 to q2, labeled with b.
4. For each input symbol a, create a transition from q1 to q2, labeled with a.
5. For each input symbol b, create a transition from q1 to q3, labeled with b.
6. For each input symbol a, create a transition from q2 to q1, labeled with a.
7. For each input symbol b, create a transition from q2 to q2, labeled with b.
8. For each input symbol a, create a transition from q3 to q2, labeled with a.
9. For each input symbol b, create a transition from q3 to q3, labeled with b.
10. Mark q3 as the final state.
The DFA constructed above has 4 states.
Therefore, the smallest number of states needed in a DFA accepting L is 4.
Hence, option B is the correct answer.
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Consider the language L given by the regular expression (a + b) *b(a +b) over the alphabet {a, b}. The smallest number of states needed in a deterministic finite-state automaton (DFA) accepting L is ______.Note:This questions appeared as Numerical Answer Type.a)3b)4c)5d)6Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the language L given by the regular expression (a + b) *b(a +b) over the alphabet {a, b}. The smallest number of states needed in a deterministic finite-state automaton (DFA) accepting L is ______.Note:This questions appeared as Numerical Answer Type.a)3b)4c)5d)6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the language L given by the regular expression (a + b) *b(a +b) over the alphabet {a, b}. The smallest number of states needed in a deterministic finite-state automaton (DFA) accepting L is ______.Note:This questions appeared as Numerical Answer Type.a)3b)4c)5d)6Correct answer is option 'B'. Can you explain this answer?.
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