On the Complexity of Infinite Advice Strings

Author Gaëtan Douéneau-Tabot

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Gaëtan Douéneau-Tabot
  • École Normale Supérieure Paris-Saclay, Université Paris-Saclay, Cachan, France

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Gaëtan Douéneau-Tabot. On the Complexity of Infinite Advice Strings. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 122:1-122:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We investigate in this paper a notion of comparison between infinite strings. In a general way, if M is a computation model (e.g. Turing machines) and C a class of objects (e.g. languages), the complexity of an infinite word alpha can be measured with respect to the amount of objects from C that are presentable with machines from M using alpha as an oracle. In our case, the model M is finite automata and the objects C are either recognized languages or presentable structures, known respectively as advice regular languages and advice automatic structures. This leads to several different classifications of infinite words that are studied in detail; we also derive logical and computational equivalent measures. Our main results explore the connections between classes of advice automatic structures, MSO-transductions and two-way transducers. They suggest a closer study of the resulting hierarchy over infinite words.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • infinite words
  • advice automata
  • automatic structures
  • transducers


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