Bulletin of the Belgian Mathematical Society - Simon Stevin

Topology and ambiguity in ω-context free languages

Olivier Finkel and Pierre Simonnet

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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

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

First available in Project Euclid: 22 January 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 68Q45: Formal languages and automata [See also 03D05, 68Q70, 94A45] 03D05: Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15] 03D55: Hierarchies 03E15: Descriptive set theory [See also 28A05, 54H05]

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


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

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