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Consider the regular language L = (111 + 11111)*. The minimum number of states in any DFA accepting this languages is:
- a)3
- b)5
- c)8
- d)9
Correct answer is option 'D'. Can you explain this answer?
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Consider the regular language L = (111 + 11111)*. The minimum number o...
The finite state automata is :
Thus, option (D) is correct.
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Please comment below if you find anything wrong in the above post.
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Consider the regular language L = (111 + 11111)*. The minimum number o...
Solution:
To find the minimum number of states in any DFA accepting this language, we need to construct a DFA for the given regular language L = (111 11111)* and minimize it using the standard DFA minimization algorithm.
Constructing DFA for L = (111 11111)*
Step 1: Start with the initial state q0.
Step 2: For each input symbol 1, create a new state and transition from the current state to the new state on input 1.
Step 3: Assume all the new states are final states.
Step 4: The final DFA will be:
q0 ---1---> q1 ---1---> q2 ---1---> q3 ---1---> q4 ---1---> q5
---1---> q6 ---1---> q7 ---1---> q8 ---1---> q9 ---1---> q10
---ε---> q11
Step 5: Mark all pairs of states (q0, q11), (q1, q6), (q2, q7), (q3, q8), (q4, q9), (q5, q10) as distinguishable.
Step 6: Repeat step 5 until no more pairs can be marked as distinguishable.
Step 7: The minimized DFA will be:
q0 ---1---> q1 ---1---> q2 ---1---> q3 ---1---> q4 ---1---> q5
---1---> q6
---ε---> q11
Step 8: The minimized DFA has 9 states, which is the minimum number of states in any DFA accepting the given regular language L.
Therefore, the correct answer is option D.
To find the minimum number of states in any DFA accepting this language, we need to construct a DFA for the given regular language L = (111 11111)* and minimize it using the standard DFA minimization algorithm.
Constructing DFA for L = (111 11111)*
Step 1: Start with the initial state q0.
Step 2: For each input symbol 1, create a new state and transition from the current state to the new state on input 1.
Step 3: Assume all the new states are final states.
Step 4: The final DFA will be:
q0 ---1---> q1 ---1---> q2 ---1---> q3 ---1---> q4 ---1---> q5
---1---> q6 ---1---> q7 ---1---> q8 ---1---> q9 ---1---> q10
---ε---> q11
Step 5: Mark all pairs of states (q0, q11), (q1, q6), (q2, q7), (q3, q8), (q4, q9), (q5, q10) as distinguishable.
Step 6: Repeat step 5 until no more pairs can be marked as distinguishable.
Step 7: The minimized DFA will be:
q0 ---1---> q1 ---1---> q2 ---1---> q3 ---1---> q4 ---1---> q5
---1---> q6
---ε---> q11
Step 8: The minimized DFA has 9 states, which is the minimum number of states in any DFA accepting the given regular language L.
Therefore, the correct answer is option D.
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Consider the regular language L = (111 + 11111)*. The minimum number of states in any DFA accepting this languages is:a)3b)5c)8d)9Correct answer is option 'D'. Can you explain this answer?
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