In the foregoing example the ambiguity came from the grammar in the sense
that it could be removed by finding an equivalent unambiguous grammar. In
some instances, however, this is not possible because the ambiguity is in the
language.
Definition 5.6
If L is a context-free language for which there exists an unambiguous grammar,
then L is said to be unambiguous. If every grammar that generates L is
ambiguous, then the language is called inherently ambiguous.
It is a somewhat difficult matter even to exhibit an inherently ambiguous
language. The best we can do here is give an example with some reasonably
plausible claim that it is inherently ambiguous.
Example 5.13
The language