Definition of a language \(L\) with alphabet \(\{a\}\) is given as following.…

GATE · 2011 · CS · Computer Science & IT

Definition of a language LL with alphabet {a}\{a\} is given as following.

L={ank∣k>0,  and  n is a positive integer constant}L = \left\{a^{nk} \mid k > 0, \:\: and \:\: n \text{ is a positive integer constant} \right\}

What is the minimum number of states needed in a DFA to recognizeLL?

  1. A.

    k+1k + 1

  2. B.

    n+1n+ 1

  3. C.

    2n+12^{n+1}

  4. D.

    2k+12^{k+1}

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