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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 FA accepting the language: L = \{ w \mid w \in \{0,1\}^* \} where the 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 states20232mFORMAL 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
PreviousConsider the following finite state automaton:  The language accepted by this automaton is given by the regular expression (i) b^*ab^*ab^*ab (ii) (a+b)^* (iii) b^*a(a+b)^* (iv) b^*ab^*abNextConsider the following languages: GATE[2005] L_1 = \{ww^R \mid w \in \{0, 1\}^*\} L_2 = \{w\#w^R \mid w \in \{0, 1\}^*\} where \# is a special symbol, L_3 = \{ww \mid w \in \{0, 1\}^*\} Which one of the following is true? (i) L_1 is a deterministic CFL (ii) L_2 is a deterministic CFL (iii) L_3 is a CFL, but not a deterministic CFL (iv) L_3 is a deterministic CFL