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Formal Language & Automata TheoryLet L = \{w \mid w \in \{0+1\}^*, w \text{ has even number of 1s}\}. Which one of the regular expression below represents L? (i) (0^* 10^* 1)^* (ii) 0^*(10^* 10^*)^* (iii) 0^* (10^* 1^*)^* 0^* (iv) 0^* 1(10^* 1)^* 10^*20202mFORMAL 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.20227mFormal Language & Automata TheoryUsing Pumping Lemma, prove that the language L = \{0^{n}1^{n} \mid n \ge 0\} is not regular.20257m Compiler DesignDefine regular expression. Write the regular expression for the language having a string which should have at least one '0' and at least one '1'.20257m
PreviousDesign deterministic finite automata for the set of strings over the alphabet \{a, b\} containing at least three occurrences of three consecutive b's, overlapping permitted (e.g., the string bbbbb should be accepted).NextAssume that a regular language L is provided to you as a DFA M(\{Q, \Sigma, \delta, q_0, F\}). How would you check whether L is infinite?
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