Solution

The correct answer is L = {anbj : n = J2} is not context free language

EXPLANATION:

• Ackermann's function is not primitive recursive.
  • The primitive recursive functions form a subset of the total recursive functions or effectively calculable functions; however, there are total recursive functions which are not primitive recursive, such as the Ackermann function.
• The language L= {anbkcn+k : n ≥ 0, k ≥ 0} is not regular.
  • Regular languages adhere to the pumping lemma, which this language would violate. Given language is a Context free language.
• L = {anbj : n = J2} is not context free language
  • This is the correct statement. The language L isn't context-free as it represents a language where the number of 'a's is equal to the square of the number of 'b's.
  • A context-free language wouldn't be able to generate or parse this kind of language, as it would require more context (like specific knowledge of numerical relationships) than a simple context-free grammar can provide. Because PDA can't able to calculation.
• For any context sensitive language L, excluding λ (the empty string), there exists a linear bounded automaton M that recognizes the language such that  L ≠ L(M).
  • This is because a context-sensitive language is defined as a language that can be recognized by a linear bounded automaton. As such, the fourth statement as it stands is incorrect.