Need help in theoretical computer science Given the following language over the alphabet Σ = {a, b, c, d}. • L = {a ^ r b ^ r c ^ r d ^ m | r, m∈IN} Answer the following questions. (i) Are infinitely...

Need help in theoretical computer science Given the following language over the alphabet Σ = {a, b, c, d}. • L = {a ^ r b ^ r c ^ r d ^ m | r, m∈IN} Answer the following questions. (i) Are infinitely many words in this language 1-inflatable? If so, include such words. (ii) Are infinitely many words in this language not 1-inflatable? If so, include such words. (iii) Can one use the pumping lemma for context-free languages ​​to show that the language L is not a context-free language? If so, briefly outline how one can then argue. Subtask (b) Now let the following language be given over the alphabet Σ = {a, b, c, d} • L = {a^r b^ r c^r d ^ m | r, m∈IN} ∪ {a^i b ^ j c^k | i, j, k∈IN} (i) Are infinitely many words in this language 1-inflatable? If so, include such words. (ii) Are infinitely many words in this language not 1-inflatable? If so, include such words. (iii) Can one use the pumping lemma for context-free languages ​​to show that the language L is not a context-free language? If so, briefly outline how one can then argue.