The Lyapunov Exponents of Reversible Cellular Automata Are Uncomputable

2019 ◽  
pp. 178-190 ◽  
Author(s):  
Johan Kopra
Keyword(s):  
Cellular Automata ◽  
Lyapunov Exponents ◽  
Reversible Cellular Automata

scholarly journals On computing the Lyapunov exponents of reversible cellular automata

2020 ◽  
Author(s):  
Johan Kopra
Keyword(s):  
Lyapunov Exponent ◽  
Cellular Automata ◽  
Lyapunov Exponents ◽  
Rational Number ◽  
Absolute Constant ◽  
Uniform Measure ◽  
Positive Rational Number ◽  
Reversible Cellular Automata

AbstractWe 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 $$2-\delta$$ 2 - δ for some absolute constant $$\delta >0$$ 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 $$\epsilon >0$$ ϵ > 0 , outputs the Lyapunov exponents of F with accuracy $$\epsilon$$ ϵ . 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 $$p,q>1$$ p , q > 1 .

Reversible cellular automata with memory of delay type

Complexity ◽  
2014 ◽  
Vol 20 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Ramón Alonso-Sanz
Keyword(s):  
Cellular Automata ◽  
Reversible Cellular Automata ◽  
With Memory

Lyapunov Exponents Vs Expansivity and Sensitivity in Cellular Automata

ACRI ’96 ◽  
1997 ◽  
pp. 57-71 ◽  
Author(s):  
Michele Finelli ◽  
Giovanni Manzini ◽  
Luciano Margara
Keyword(s):  
Cellular Automata ◽  
Lyapunov Exponents

scholarly journals BLOCK CIPHERS ON THE BASIS OF REVERSIBLE CELLULAR AUTOMATA

2020 ◽  
Vol 10 (1) ◽  
pp. 8-11
Author(s):  
Yuliya Tanasyuk ◽  
Petro Burdeinyi
Keyword(s):  
Cellular Automata ◽  
Block Cipher ◽  
Key Generation ◽  
One Dimensional ◽  
C Programming Language ◽  
C Programming ◽  
Shared Secret ◽  
Reversible Cellular Automata ◽  
The Given ◽  
First Time

The given paper is devoted to the software development of block cipher based on reversible one-dimensional cellular automata and the study of its statistical properties. The software implementation of the proposed encryption algorithm is performed in C# programming language in Visual Studio 2017. The paper presents specially designed approach for key generation. To ensure desired cryptographic stability, the shared secret parameters can be adjusted to contain information needed for creating substitution tables, defining reversible rules, and hiding final data. For the first time, it is suggested to create substitution tables based on iterations of a cellular automaton that is initialized by the key data.

Pattern formation in reversible cellular automata

1986 ◽  
Vol 19 (15) ◽  
pp. L933-L939 ◽  
Author(s):  
J Vinals ◽  
J D Gunton
Keyword(s):  
Pattern Formation ◽  
Cellular Automata ◽  
Reversible Cellular Automata
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