Undecidable word problem in subshift automorphism groups

This article studies the complexity of the word problem in groups of automorphisms of subshifts. We show in particular that for any Turing degree, there exists a subshift whose automorphism group contains a subgroup whose word problem has exactly this degree.

[1]  Marie-Pierre Béal,et al.  Decidability of Conjugacy of Tree-Shifts of Finite Type , 2009, ICALP.

[2]  Van Cyr,et al.  THE AUTOMORPHISM GROUP OF A SHIFT OF LINEAR GROWTH: BEYOND TRANSITIVITY , 2014, Forum of Mathematics, Sigma.

[3]  S. G. Simpson.  Medvedev degrees of two-dimensional subshifts of finite type , 2012, Ergodic Theory and Dynamical Systems.

[4]  Dale Myers,et al.  Nonrecursive tilings of the plane. II , 1974, Journal of Symbolic Logic.

[5]  Jarkko Kari,et al.  Reversibility and Surjectivity Problems of Cellular Automata , 1994, J. Comput. Syst. Sci..

[6]  Michael Hochman,et al.  On the automorphism groups of multidimensional shifts of finite type , 2009, Ergodic Theory and Dynamical Systems.

[7]  Jarkko Kari,et al.  Finite generating sets for reversible gate sets under general conservation laws , 2017, Theor. Comput. Sci..

[8]  William P. Hanf,et al.  Nonrecursive tilings of the plane. I , 1974, Journal of Symbolic Logic.

[9]  M. Rabin.  Computable algebra, general theory and theory of computable fields. , 1960 .

[10]  Jarkko Kari,et al.  Periodicity and Immortality in Reversible Computing , 2008, MFCS.

[11]  A. Maass,et al.  On automorphism groups of low complexity subshifts , 2015, Ergodic Theory and Dynamical Systems.

[12]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[13]  Nathalie Aubrun,et al.  A notion of effectiveness for subshifts on finitely generated groups , 2014, Theor. Comput. Sci..

[14]  B. H. Mayoh.  Review: M. O. Rabin, Computable Algebraic Systems; Michael O. Rabin, Computable Algebra, General Theory and Theory of Computable Fields , 1967 .

[15]  Jr. Hartley Rogers.  Theory of Recursive Functions and Effective Computability , 1969 .

[16]  Douglas Lind,et al.  The automorphism group of a shift of finite type , 1988 .

[17]  G. A. Hedlund.  Endomorphisms and automorphisms of the shift dynamical system , 1969, Mathematical systems theory.