Topology and ambiguity in ω-context free languages

Abstract

We study the links between the topological complexity of an$\omega$-context free language and its degree of ambiguity.In particular, using known facts from classicaldescriptive set theory, we prove that non Borel $\omega$-context free languages which are recognized by Büchipushdown automata have a maximum degree of ambiguity.This result implies that degrees of ambiguity are really not preserved bythe operation$W \rightarrow W^\omega$, defined over finitary context free languages.We prove also that taking the adherence or the $\delta$-limit of a finitarylanguagepreserves neither ambiguity nor inherent ambiguity. On the other side we show that methods used in the study of$\omega$-context free languagescan also be applied to study the notion of ambiguity ininfinitary rational relations accepted by Büchi 2-tape automataand we get first results in that direction.