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An {omega}-language is a set of infinite words over a finite alphabet X. We consider the class of recursive {omega}-languages, i.e. the class of {omega}-languages accepted by Turing machines with a Buchi acceptance condition, which is also the class {Sigma}11 of (effective) analytic subsets of X{omega} for some finite alphabet X. We investigate here the notion of ambiguity for recursive {omega}-languages with regard to acceptance by Buchi Turing machines. We first present in detail essentials on the literature on {omega}-languages accepted by Turing Machines. Then we give a complete and broad view on the notion of ambiguity and unambiguity of Buchi Turing machines and of the {omega}-languages they accept. To obtain our new results, we make use of results and methods of effective descriptive set theory.
We survey recent results on the topological complexity of context-free omega-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-
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 ar
This is an extended abstract presenting new results on the topological complexity of omega-powers (which are included in a paper Classical and effective descriptive complexities of omega-powers available from arXiv:0708.4176) and reflecting also some
We show that, from a topological point of view, considering the Borel and the Wadge hierarchies, 1-counter Buchi automata have the same accepting power than Turing machines equipped with a Buchi acceptance condition. In particular, for every non null
We prove in this paper that the length of the Wadge hierarchy of omega context free languages is greater than the Cantor ordinal epsilon_omega, which is the omega-th fixed point of the ordinal exponentiation of base omega. The same result holds for t