Examples
An example of a context-sensitive language that is not context-free is L = { ap : p is a prime number }. L can be shown to be a context-sensitive language by constructing a linear bounded automaton which accepts L. The language can easily be shown to be neither regular nor context free by applying the respective pumping lemmas for each of the language classes to L.
An example of recursive language that is not context-sensitive is any recursive language whose decision is an EXPSPACE-hard problem, say, the set of pairs of equivalent regular expressions with exponentiation.
Read more about this topic: Context-sensitive Language
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