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How many minimum number of states are required in the DFA (over the alphabet {a, b}) accepting all the strings with the number of a’s divisible by 4 and number of b’s divisible by 5?
  • a)
    20
  • b)
    9
  • c)
    7
  • d)
    15
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
How many minimum number of states are required in the DFA (over the al...
For DFA accepting all the strings with number of a’s divisible by 4; four states are required similarly for DFA accepting all the strings with number of b’s divisible by 5, five states are required and for their combination, states will be multiplied. So 5 x 4 = 20 states will be required.
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How many minimum number of states are required in the DFA (over the al...
To construct a DFA that accepts all strings with an even number of 'a's, we need a minimum of 2 states.

State 1: Initial state
- When reading 'a', transition to State 2
- When reading 'b', stay in State 1

State 2: Accepting state
- When reading 'a', transition back to State 1
- When reading 'b', stay in State 2

State 1 is the initial state and State 2 is the accepting state. This DFA will accept any string with an even number of 'a's and reject any string with an odd number of 'a's.
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Community Answer
How many minimum number of states are required in the DFA (over the al...
20
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How many minimum number of states are required in the DFA (over the alphabet {a, b}) accepting all the strings with the number of a’s divisible by 4 and number of b’s divisible by 5?a)20b)9c)7d)15Correct answer is option 'A'. Can you explain this answer?
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