Some inherently ambiguous context-free languages

We prove the inherent ambiguity of certain context-free languages, the prototype of which is L = {s 2 t | t = υ^′ over(s, -) υ, s, υ, υ^′ ∈ {0, 1}*} , (over(s,-) is the reflection of s). Actually, we prove that in general the degree of ambiguity of ent is, as expected, at least the number of factorizations t = υ^′ over(s, -) υ. We also prove inherent direct ambiguity (of infinite degree) of certain languages, and the recursive unsolvability of that property.