The Lyapunov Exponents of Reversible Cellular Automata Are Uncomputable



: Kopra J.

: Ian McQuillan, Shinnosuke Seki

: International Conference on Unconventional Computation and Natural Computation

Publisher: Springer Verlag

: 2019

: Lecture Notes in Computer Science

: Unconventional Computation and Natural Computation : 18th International Conference, UCNC 2019, Tokyo, Japan, June 3–7, 2019, Proceedings

: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

: Lecture Notes in Computer Science

: 11493

: 978-3-030-19310-2

: 978-3-030-19311-9

: 0302-9743

DOI: https://doi.org/10.1007/978-3-030-19311-9_15

: https://research.utu.fi/converis/portal/detail/Publication/41254647


We will show that the class of reversible cellular automata (CA) with right Lyapunov exponent 2 cannot be separated algorithmically from the class of reversible CA whose right Lyapunov exponents are at most 2−δ for some absolute constant δ>0. Therefore there is no algorithm that, given as an input a description of an arbitrary reversible CA F and a positive rational number ϵ>0, outputs the Lyapunov exponents of F with accuracy ϵ.


Last updated on 2024-26-11 at 12:48