The Lyapunov Exponents of Reversible Cellular Automata Are Uncomputable

  • Johan KopraEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11493)


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 \(2-\delta \) for some absolute constant \(\delta >0\). Therefore there is no algorithm that, given as an input a description of an arbitrary reversible CA F and a positive rational number \(\epsilon >0\), outputs the Lyapunov exponents of F with accuracy \(\epsilon \).


Cellular automata Lyapunov exponents Reversible computation Computability 


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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

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