Bulletin of the Belgian Mathematical Society - Simon Stevin

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 classical descriptive set theory, we prove that non Borel $\omega$-context free languages which are recognized by Büchi pushdown automata have a maximum degree of ambiguity. This result implies that degrees of ambiguity are really not preserved by the operation $W \rightarrow W^\omega$, defined over finitary context free languages. We prove also that taking the adherence or the $\delta$-limit of a finitary language preserves neither ambiguity nor inherent ambiguity. On the other side we show that methods used in the study of $\omega$-context free languages can also be applied to study the notion of ambiguity in infinitary rational relations accepted by Büchi 2-tape automata and we get first results in that direction.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 10, Number 5 (2003), 707-722.

Dates
First available in Project Euclid: 22 January 2004

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1074791327

Digital Object Identifier
doi:10.36045/bbms/1074791327

Mathematical Reviews number (MathSciNet)
MR2073022

Zentralblatt MATH identifier
1080.68054

Citation

Finkel, Olivier; Simonnet, Pierre. Topology and ambiguity in ω-context free languages. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), no. 5, 707--722. doi:10.36045/bbms/1074791327. https://projecteuclid.org/euclid.bbms/1074791327