On repetition languages

Orna Kupferman, Ofer Leshkowitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

A regular language R of finite words induces three repetition languages of infinite words: the language lim(R), which contains words with infinitely many prefixes in R, the language ∞R, which contains words with infinitely many disjoint subwords in R, and the language Rω, which contains infinite concatenations of words in R. Specifying behaviors, the three repetition languages provide three different ways of turning a specification of a finite behavior into an infinite one. We study the expressive power required for recognizing repetition languages, in particular whether they can always be recognized by a deterministic Büchi word automaton (DBW), the blow up in going from an automaton for R to automata for the repetition languages, and the complexity of related decision problems. For lim R and ∞R, most of these problems have already been studied or are easy. We focus on Rω. Its study involves some new and interesting results about additional repetition languages, in particular R#, which contains exactly all words with unboundedly many concatenations of words in R. We show that Rω is DBW-recognizable iff R# is ω-regular iff R# = Rω, and there are languages for which these criteria do not hold. Thus, Rω need not be DBW-recognizable. In addition, when exists, the construction of a DBW for Rω may involve a 2O(n log n) blow-up, and deciding whether Rω is DBW-recognizable, for R given by a nondeterministic automaton, is PSPACE-complete. Finally, we lift the difference between R# and Rω to automata on finite words and study a variant of Büchi automata where a word is accepted if (possibly different) runs on it visit accepting states unboundedly many times.

Original languageAmerican English
Title of host publication45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020
EditorsJavier Esparza, Daniel Kral�, Daniel Kral�
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771597
DOIs
StatePublished - 1 Aug 2020
Event45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020 - Prague, Czech Republic
Duration: 25 Aug 202026 Aug 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume170
ISSN (Print)1868-8969

Conference

Conference45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020
Country/TerritoryCzech Republic
CityPrague
Period25/08/2026/08/20

Bibliographical note

Publisher Copyright:
© Nathalie Bertrand; licensed under Creative Commons License CC-BY 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020).

Keywords

  • Büchi automata
  • Expressive power
  • Succinctness

Fingerprint

Dive into the research topics of 'On repetition languages'. Together they form a unique fingerprint.

Cite this