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Article Dans Une Revue Bulletin of the Belgian Mathematical Society Année : 2003

Topology and Ambiguity in Omega Context Free Languages

Olivier Finkel
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Pierre Simonnet
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Résumé

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 of taking the omega power of a finitary context free language. We prove also that taking the adherence or the delta-limit of a finitary language preserves neither unambiguity 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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Dates et versions

hal-00109923 , version 1 (26-10-2006)
hal-00109923 , version 2 (03-01-2008)

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Olivier Finkel, Pierre Simonnet. Topology and Ambiguity in Omega Context Free Languages. Bulletin of the Belgian Mathematical Society, 2003, 10 (5), pp.707-722. ⟨hal-00109923v2⟩
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