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FORMAL LANGUAGE & AUTOMATA THEORYDesign a DFA for strings over \{a, b\} containing at least three occurrences of bbb (overlapping allowed). Example: bbbbbb is accepted.20227mFORMAL LANGUAGE & AUTOMATA THEORYConstruct an NFA that accepts all strings over the alphabet {0, 1, 2} that begin with one or more 0s, followed by an odd number of 1s, and end with any number of 2s.20257mFormal Language & Automata TheoryWhat is the minimum number of states in deterministic finite automata (DFA) for string starting with ba^2 and ending with a over alphabet \{a, b\}? (i) Ten (ii) Nine (iii) Eight (iv) Six20202mFORMAL LANGUAGE & AUTOMATA THEORYLet L \subseteq \{0,1,2\}^* be strings without consecutive identical symbols (no 00, no 11, no 22). Design a DFA for L.20227m