Unambiguous Turn Position and Rational Trace Languages

We show the existence of rational trace languages defined over direct products of free monoids that have inherent ambiguity of the order of log n and n 1/2 . This result is obtained by studying the relationship between trace languages and linear context-free grammars that satisfy a special unambiguity condition on the position of the last step of derivation

Universal Inherence of cycle-free context-free Ambiguity Functions

It is shown that the set of inherent ambiguity functions for context-free languages and the set of ambiguity functions for cycle-free context-free grammars coincide. Moreover for each census function of an unambiguous context-free language the least monotone function larger than or equal to is an inherent ambiguity function. Both results are based on a more general theorem. Informally it states that the loss of information induced by a length preserving homomorphism on an unambiguous context-free language can be turned into inherent ambiguity