Ambiguity of $\omega$-Languages of Turing Machines

Olivier Finkel (1, 2)

1 ELM - Équipe de Logique Mathématique
2 IMJ - Institut de Mathématiques de Jussieu

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 Büchi acceptance condition, which is also the class $\Sigma_1^1$ 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 Büchi 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 Büchi 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.

Mots clés: models of set theory; Automata and formal languages; infinite words; Turing machines; Büchi transition systems; ambiguity; degrees of ambiguity; logic in computer science; effective descriptive set theory

Domaines: Logique en informatique [cs.LO]; Complexité [cs.CC]; Logique [math.LO]

Olivier Finkel. Ambiguity of $\omega$-Languages of Turing Machines. Logical Methods in Computer Science, 2014, 10 (3:12), pp.1-18. ⟨hal-00735050v2⟩