Turing degree spectra of minimal subshifts

Michael Hochman; Pascal Vanier

doi:10.1007/978-3-319-58747-9_15

Turing degree spectra of minimal subshifts

Michael Hochman
, Pascal Vanier^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Scopus citations

Abstract

Subshifts are shift invariant closed subsets of Σ^Z^d, 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 language	English
Title of host publication	Computer Science - Theory and Applications - 12th International Computer Science Symposium in Russia, CSR 2017, Proceedings
Editors	Pascal Weil
Publisher	Springer Verlag
Pages	154-161
Number of pages	8
ISBN (Print)	9783319587462
DOIs	https://doi.org/10.1007/978-3-319-58747-9_15
State	Published - 2017
Event	12th International Computer Science Symposium in Russia, CSR 2017 - Kazan, Russian Federation Duration: 8 Jun 2017 → 12 Jun 2017

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10304 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	12th International Computer Science Symposium in Russia, CSR 2017
Country/Territory	Russian Federation
City	Kazan
Period	8/06/17 → 12/06/17

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017.

Access to Document

10.1007/978-3-319-58747-9_15

Cite this

Hochman, M., & Vanier, P. (2017). Turing degree spectra of minimal subshifts. In P. Weil (Ed.), Computer Science - Theory and Applications - 12th International Computer Science Symposium in Russia, CSR 2017, Proceedings (pp. 154-161). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10304 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-58747-9_15

Hochman, Michael ; Vanier, Pascal. / Turing degree spectra of minimal subshifts. Computer Science - Theory and Applications - 12th International Computer Science Symposium in Russia, CSR 2017, Proceedings. editor / Pascal Weil. Springer Verlag, 2017. pp. 154-161 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Hochman, M & Vanier, P 2017, Turing degree spectra of minimal subshifts. in P Weil (ed.), Computer Science - Theory and Applications - 12th International Computer Science Symposium in Russia, CSR 2017, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10304 LNCS, Springer Verlag, pp. 154-161, 12th International Computer Science Symposium in Russia, CSR 2017, Kazan, Russian Federation, 8/06/17. https://doi.org/10.1007/978-3-319-58747-9_15

Turing degree spectra of minimal subshifts. / Hochman, Michael; Vanier, Pascal.
Computer Science - Theory and Applications - 12th International Computer Science Symposium in Russia, CSR 2017, Proceedings. ed. / Pascal Weil. Springer Verlag, 2017. p. 154-161 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10304 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Hochman M, Vanier P. Turing degree spectra of minimal subshifts. In Weil P, editor, Computer Science - Theory and Applications - 12th International Computer Science Symposium in Russia, CSR 2017, Proceedings. Springer Verlag. 2017. p. 154-161. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-58747-9_15

Turing degree spectra of minimal subshifts

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