GATE | GATE CS 2019 | Question 57

Let Σ be the set of all bijections from {1, …, 5} to {1, …, 5}, where id denotes the identity function, i.e. id(j) = j,∀j. Let ° denote composition on functions. For a string x = x1x2 … xn ∈ Σn, n ≥ 0, let π(x) = x1°x2° … °xn.

Consider the language L = {x ∈ Σ* ⏐ π(x) = id}. The minimum number of states in any DFA accepting L is _________ .

Note: This was Numerical Type question.
(A) 120
(B) 125
(C) 210
(D) None of these


Answer: (A)

Explanation: The DFA for accepting L will have 5! = 120 states, since we need one state for every possible permutation function on 5 elements.

So, answer is 120.

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