Which of the following sets can be recognized by a Deterministic Finite-state Automaton?
(A) The number 1, 2, 4, 8……,2^n,………. written in binary.
(B) The number 1, 2, 4,….., 2^n,………. written in unary.
(C) The set of binary strings in which the number of zeros is the same as the number of ones.
(D) The set {1, 101, 11011, 1110111,…….}
Answer: (A)
Explanation: If there is a infinite language and for that language if their is no any pattern exist then we can surely say that given language is not regular, but if pattern is exist for that language then it may or may not be regular language and for ensuring a given language is regular, if we are able to draw DFA for that language then surely it will be regular otherwise not regular,
Therefore option (A) is regular language as it can written in binary i.e.,
L = {1, 10, 100, 1000, 10000, …} Regular expression is (10*), since, for this expression we can draw DFA.
So, option (A) is correct.
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