Turing degree spectra of minimal subshifts

Michael Hochman, Pascal Vanier*

*Corresponding author for this work

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

6 Scopus citations


Subshifts are shift invariant closed subsets of ΣZd, with Σ a finite alphabet. Minimal subshifts are subshifts in which all points contain the same patterns. It has been proved by Jeandel and Vanier that the Turing degree spectra of non-periodic minimal subshifts always contain the cone of Turing degrees above any of its degrees. It was how-ever not known whether each minimal subshift’s spectrum was formed of exactly one cone or not. We construct inductively a minimal subshift whose spectrum consists of an uncountable number of cones with incom-parable bases.

Original languageAmerican English
Title of host publicationComputer Science - Theory and Applications - 12th International Computer Science Symposium in Russia, CSR 2017, Proceedings
EditorsPascal Weil
PublisherSpringer Verlag
Number of pages8
ISBN (Print)9783319587462
StatePublished - 2017
Event12th International Computer Science Symposium in Russia, CSR 2017 - Kazan, Russian Federation
Duration: 8 Jun 201712 Jun 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10304 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference12th International Computer Science Symposium in Russia, CSR 2017
Country/TerritoryRussian Federation

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017.


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