Undecidable word problem in subshift automorphism groups
: Guillon P., Jeandel E., Kari J., Vanier P.
: van Bevern R., Kucherov G.
: International Computer Science Symposium in Russia
Publisher: Springer Verlag
: 2019
: Lecture Notes in Computer Science
: Computer Science – Theory and Applications. CSR 2019
: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
: Lecture Notes in Computer Science
: 11532
: 180
: 190
: 978-3-030-19954-8
: 978-3-030-19955-5
DOI: https://doi.org/10.1007/978-3-030-19955-5_16
: 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.
