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Formal Language & Automata TheoryDefinition of a language L with alphabet \{a\} is given as L= \{a^{nk} / k > 0, \text{ and } n \text{ is a positive integer constant}\}. What is the minimum number of states needed in a DFA to recognize L? (i) k + 1 (ii) n + 1 (iii) 2n + 1 (iv) 2k + 120222mFORMAL LANGUAGE & AUTOMATA THEORYFor an NFA with n states, the minimized DFA has: (i) m \le 2^n (ii) n \le m (iii) one accept state (iv) m = 2^n20212mFormal Language & Automata TheoryConsider the regular expression (0+1)(0+1)\dots N \text{ times}. The minimum state FA that recognizes the language represented by this regular expression contains (i) n states (ii) (n+1) states (iii) (n+2) states (iv) None of the above20192mFormal 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^n20212m