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December 2003 Topology and ambiguity in ω-context free languages
Olivier Finkel, Pierre Simonnet
Bull. Belg. Math. Soc. Simon Stevin 10(5): 707-722 (December 2003). DOI: 10.36045/bbms/1074791327


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.


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Olivier Finkel. Pierre Simonnet. "Topology and ambiguity in ω-context free languages." Bull. Belg. Math. Soc. Simon Stevin 10 (5) 707 - 722, December 2003.


Published: December 2003
First available in Project Euclid: 22 January 2004

zbMATH: 1080.68054
MathSciNet: MR2073022
Digital Object Identifier: 10.36045/bbms/1074791327

Primary: 03D05 , 03D55 , 03E15 , 68Q45

Keywords: ambiguity , analytic sets , borel hierarchy , context free languages , degrees of ambiguity , infinitary rational relations , infinite words , topological properties

Rights: Copyright © 2003 The Belgian Mathematical Society


Vol.10 • No. 5 • December 2003
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