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Automaton accepting the regular expression of any number of a ‘ s is:
  • a)
    a*
  • b)
    ab*
  • c)
    (a/b)*
  • d)
    a*b*c
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Automaton accepting the regular expression of any number of a ‘ ...
It gives any number of a’s.
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Automaton accepting the regular expression of any number of a ‘ ...
An automaton that accepts the regular expression of any number of 'a' can be represented using a deterministic finite automaton (DFA) as follows:

- The DFA will have only one initial state, q0.
- There will be a single accepting state, q1.
- The transition function will define the behavior of the automaton for each input symbol.
- For the input symbol 'a', the automaton will transition from q0 to q0.
- For any other input symbol, the automaton will stay in q0.
- The automaton will stay in q0 for any number of 'a's.
- Once the input ends, if the automaton is in q0, it will transition to q1.

Formally, the DFA can be described as follows:

Q = {q0, q1} - set of states
Σ = {'a', other symbols} - input alphabet
δ = transition function:
δ(q0, 'a') = q0
δ(q0, other symbols) = q0
δ(q1, all symbols) = q1
q0 = initial state
F = {q1} - set of accepting states

This automaton will accept any input string that consists of any number of 'a's (including an empty string).
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