Final answer:
Determining whether two context-free languages recognize the same language can be complex and requires analyzing the grammars and converting them to Chomsky normal form. Algorithms like CYK or Earley parser can be used to check for equivalence. If the grammars are not equivalent, determining if one language is a subset of the other is a more difficult problem known as the language inclusion problem.
Step-by-step explanation:
Determining whether two context-free languages recognize the same language can be a complex task. It requires analyzing the grammars of the languages and checking if they generate the same set of strings. One approach to determine this is to convert the grammars into their respective Chomsky normal form and compare them for equivalence using algorithms like the CYK algorithm or the Earley parser. If the two grammars are equivalent, then the languages they recognize are the same. However, if the grammars are not equivalent, it can still be difficult to determine whether the languages they generate overlap or if one language is a subset of the other. This problem is known as the language inclusion problem and requires advanced techniques to solve.