A4 Article in conference proceedings
The Lyapunov Exponents of Reversible Cellular Automata Are Uncomputable
List of Authors: Kopra J.
Conference name: International Conference on Unconventional Computation and Natural Computation
Publisher: Springer Verlag
Publication year: 2019
Journal: Lecture Notes in Computer Science
Book title *: Unconventional Computation and Natural Computation : 18th International Conference, UCNC 2019, Tokyo, Japan, June 3–7, 2019, Proceedings
Journal name in source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Title of series: Lecture Notes in Computer Science
Volume number: 11493
ISBN: 978-3-030-19310-2
eISBN: 978-3-030-19311-9
ISSN: 0302-9743
DOI: http://dx.doi.org/10.1007/978-3-030-19311-9_15
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.
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