A4 Refereed article in a conference publication
Undecidable word problem in subshift automorphism groups
Authors: Guillon P., Jeandel E., Kari J., Vanier P.
Editors: van Bevern R., Kucherov G.
Conference name: International Computer Science Symposium in Russia
Publisher: Springer Verlag
Publication year: 2019
Journal: Lecture Notes in Computer Science
Book title : Computer Science – Theory and Applications. CSR 2019
Journal name in source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Series title: Lecture Notes in Computer Science
Volume: 11532
First page : 180
Last page: 190
ISBN: 978-3-030-19954-8
eISBN: 978-3-030-19955-5
DOI: https://doi.org/10.1007/978-3-030-19955-5_16
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/42007423
This article studies the complexity of the word problem in groups of automorphisms (or reversible cellular automata) of subshifts. We show in particular that for any computably enumerable Turing degree, there exists a (two-dimensional) subshift of finite type whose automorphism group contains a subgroup whose word problem has exactly this degree. In particular, there are such subshifts of finite type where this problem is uncomputable. This remains true in a large setting of subshifts over groups.
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