  GF(2)-grammars are a recently introduced grammar family with some unusual
algebraic properties. They are closely connected to unambiguous grammars. By
using the method of formal power series, we establish strong conditions that
are necessary for subsets of a^* b^* and a^* b^* c^* to be described by some
GF(2)-grammar. By further applying the established results, we settle the
long-standing open question of proving inherent ambiguity of the language {a^n
b^m c^k | n != m or m != k}$, as well as give a new purely algebraic proof of
the inherent ambiguity of the language {a^n b^m c^k}{n = m or m = k}.
