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FORMAL LANGUAGE & AUTOMATA THEORYShow that the language: L = \{ a^{n!} : n \ge 0 \} is not regular or not context-free.20217mFormal Language & Automata TheoryProve that the language L = \{a^{i^2} \mid i \ge 1\} is not context-free language.20197mFORMAL LANGUAGE & AUTOMATA THEORYShow that the language: L = \{ a^{n^2} b^n \mid n \ge 0 \} is not regular.20227mFORMAL LANGUAGE & AUTOMATA THEORYUse the pumping lemma to prove that the language L = \{a^n b^n : n \ge 1\} is not regular.20257m
PreviousSuppose L is context free and R is regular, justify your answer with the help of example: (i) Is L-R necessarily context free? (ii) Is R-L necessarily context free?NextLet G be a context-free grammar in Chomsky normal form that contains b variable. Show that if G generates some string using a derivation with at least 2^b steps, then L(G) is infinite.
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