Topological Complexity of Context-Free omega-Languages: A Survey
Olivier Finkel (ELM, IMJ, LIP)
TL;DR
This survey reviews recent research on the topological complexity of context-free omega-languages, focusing on hierarchies, decision problems, ambiguity, and omega-powers within the Chomsky hierarchy.
Contribution
It provides a comprehensive overview of the current state of knowledge on the topological and decision-theoretic aspects of context-free omega-languages.
Findings
Analysis of Borel and Wadge hierarchies for omega-languages
Connections between ambiguity and topological complexity
Insights into decision problems and omega-powers
Abstract
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-deterministic or deterministic context-free omega-languages. We study also decision problems, the links with the notions of ambiguity and of degrees of ambiguity, and the special case of omega-powers.
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Taxonomy
Topicssemigroups and automata theory · Computability, Logic, AI Algorithms · Advanced Algebra and Logic