We consider the problem of computing the Lyapunov exponents of reversible cellular automata (CA). We show that the class of reversible 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 \(\epsilon\). We also compute the average Lyapunov exponents (with respect to the uniform measure) of the reversible CA that perform multiplication by p in base pq for coprime \(p,q>1\).

我们考虑计算可逆细胞自动机（CA）的Lyapunov指数的问题。我们证明，对于某些绝对常数\（\ delta> 0 \），具有正确的Lyapunov指数2的可逆CA的类不能从算法上与其正确的Lyapunov指数最大为\（2- \ delta \）的可逆CA的类分开。。因此，没有一种算法给出给定的任意可逆CA F和正有理数\（\ epsilon> 0 \）的输入，而输出的F的Lyapunov指数的精度为\（\ epsilon \）。我们还计算了执行乘以的可逆CA的平均Lyapunov指数（相对于均匀度量）共质数\（p，q> 1 \）的基pq中的p。