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Formal Language & Automata TheoryA minimum state deterministic FA accepting the language L = \{w \mid w \in \{0, 1\}^*\} where number of 0's and 1's in w are divisible by 3 and 5 respectively, has (i) 15 states (ii) 11 states (iii) 10 states (iv) 9 states20212mFormal Language & Automata TheoryA minimum state deterministic finite automaton accepting the language L = \{w \mid w \in \{0, 1\}^*, \text{ number of 0's and 1's in } w \text{ are divisible by 3 and 5 respectively}\} has (i) 15 states (ii) 11 states (iii) 10 states (iv) 9 states20192mFORMAL 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 states20212mFormal 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 above20192m
PreviousLet 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^nNextThe language \{ a^n b^n c^{n+m} \mid m, n \ge 1 \} is: (i) regular (ii) context-free but not regular (iii) context-sensitive but not context-free (iv) type 0 but not context-sensitive