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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 TheoryLet w be any string of length n in \{0, 1\}^*. Let L be the set of all substrings of w. What is the minimum number of states in a non-deterministic FA that accepts L? (i) n - 1 (ii) n (iii) n + 1 (iv) 2n - 120192mFormal 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 THEORYA minimum state DFA for the language: L = \{ w \in \{0,1\}^* : \#0(w) \equiv 0 \mod 3,\; \#1(w) \equiv 0 \mod 5 \} has: (i) 15 states (ii) 11 states (iii) 10 states (iv) 9 states20212m
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