Sublinear Ambiguity

Abstract

A context-free grammar G is ambiguous if there is a word that can be generated by G with at least two different derivation trees. Ambiguous grammars are often distinguished by their degree of ambiguity, which is the maximal number of derivation trees for the words generated by them. If there is no such upper bound G is said to be ambiguous of infinite degree. By considering how many derivation trees a word of at most length n may have, we can distinguish context-free grammars with infinite degree of ambiguity by the growth-rate of their ambiguity with respect to the length of the words. It is known that each cycle-free context-free grammar G is either exponentially ambiguous or its ambiguity is bounded by a polynomial. Until now there have only been examples of context-free languages with inherent ambiguity 2^Θ(n) and Θ(n ^d) for each d ∈ N₀. In this paper first examples of (linear) context-free languages with nonconstant sublinear ambiguity are presented.