Ambiguity of {\omega}-Languages of Turing Machines

TL;DR

This paper explores the ambiguity in recursive {}-languages accepted by B00uchi Turing machines, using effective descriptive set theory to analyze their acceptance properties and classify their ambiguity levels.

Contribution

It provides a comprehensive analysis of ambiguity in recursive {}-languages accepted by B00uchi Turing machines, including new classifications and theoretical insights.

Findings

Detailed literature review on {}-languages accepted by Turing machines.

Broad view and classification of ambiguity in B00uchi Turing machine acceptance.

Application of effective descriptive set theory to analyze ambiguity properties.

Abstract

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 B\"uchi 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 B\"uchi 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 B\"uchi 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.