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FORMAL LANGUAGE & AUTOMATA THEORYLet N be an NFA with n states and let M be the minimized DFA with m states recognizing the same language. Which of the following is necessarily true? (i) m \le 2^n (ii) n \le m (iii) M has one accept state (iv) m = 2^n20232mFormal Language & Automata TheoryLet N be an NFA with n states and let M be the minimized DFA with m states recognizing the same language. Which of the following is necessarily true? (i) m \le 2^n (ii) n \le m (iii) M has one accept state (iv) m = 2^n20212mDiscrete MathematicsProve the following by using the principle of mathematical induction for all n \in N: 1^3 + 2^3 + 3^3 + \dots + n^3 = \left(\frac{n(n+1)}{2}\right)^2202314mDesign & Analysis of AlgorithmsIn the following C++ function, let n >= m. ``cpp int gcd(int n, int m) { if (n % m == 0) return m; if (n < m) swap(n, m); while (m > 0) { n = n % m; swap(n, m); } return n; } `` What is the time complexity of the above function assuming n > m? - (i) \Theta(\log n) - (ii) \Omega(n) - (iii) \Theta(\log \log n) - (iv) \Theta(\sqrt{n})20192m
PreviousWhich of the following statements regarding sets is false? (i) A \cap A = A (ii) A \cup A = A (iii) A - (B \cap C) = (A - B) \cup (A - C) (iv) (A \cup B)' = A' \cup B'NextA simple graph can have (i) multiple edges (ii) self-loops (iii) parallel edges (iv) no multiple edges, self-loops and parallel edges
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