Topological Complexity of Context-Free ω-Languages: A Survey
نویسنده
چکیده
We survey recent results on the topological complexity of context-free ω-languages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge hierarchy of non-deterministic or deterministic context-free ω-languages. We study also decision problems, the links with the notions of ambiguity and of degrees of ambiguity, and the special case of ω-powers.
منابع مشابه
Topological Complexity of Context-Free omega-Languages: A Survey
We survey recent results on the topological complexity of context-free ω-languages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge hierarchy of non-deterministic or deterministic context-free ω-languages. We study also decision problems, the links with the notions of ambiguity and of degrees of amb...
متن کاملTopological Complexity of omega-Powers: Extended Abstract
The operation V → V ω is a fundamental operation over finitary languages leading to ω-languages. It produces ω-powers, i.e. ω-languages in the form V , where V is a finitary language. This operation appears in the characterization of the class REGω of ω-regular languages (respectively, of the class CFω of context free ω-languages) as the ω-Kleene closure of the family REG of regular finitary la...
متن کاملen sl - 0 01 57 20 4 , v er si on 1 - 2 5 Ju n 20 07 There exist some ω - powers of any Borel rank
The operation V → V ω is a fundamental operation over finitary languages leading to ω-languages. Since the set Σ of infinite words over a finite alphabet Σ can be equipped with the usual Cantor topology, the question of the topological complexity of ω-powers of finitary languages naturally arises and has been posed by Niwinski [Niw90], Simonnet [Sim92] and Staiger [Sta97a]. It has been recently...
متن کاملThere Exist Some omega -Powers of Any Borel Rank
The operation V → V ω is a fundamental operation over finitary languages leading to ω-languages. Since the set Σ of infinite words over a finite alphabet Σ can be equipped with the usual Cantor topology, the question of the topological complexity of ω-powers of finitary languages naturally arises and has been posed by Niwinski [Niw90], Simonnet [Sim92] and Staiger [Sta97a]. It has been recently...
متن کاملTopology and ambiguity in ω-context free languages
We study the links between the topological complexity of an ω-context free language and its degree of ambiguity. In particular, using known facts from classical descriptive set theory, we prove that non Borel ω-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 o...
متن کامل