Nonlinear Sciences > Cellular Automata and Lattice Gases
[Submitted on 8 Feb 2024 (v1), last revised 27 Jul 2024 (this version, v2)]
Title:Two Graphs: Resolving the Periodic Reversibility of One-dimensional Finite Cellular Automata
View PDF HTML (experimental)Abstract:Finite cellular automata (FCA) are widely used in simulating nonlinear complex systems, and their reversibility is closely related to information loss during the evolution. However, only a relatively small portion of their reversibility problems has been solved. In this paper, we perform calculations on two graphs and discover that the reversibility of any one-dimensional FCA exhibits periodicity as the number of cells increases. We also successfully provide a method to compute the reversibility sequence that encompasses the reversibility of one-dimensional FCA with any number of cells. Additionally, the calculations in this paper are applicable to FCA with various types of boundaries. This means that we will have an efficient method to determine the reversibility of almost all one-dimensional FCA, with a complexity independent of cell number.
Submission history
From: Chen Wang [view email][v1] Thu, 8 Feb 2024 04:46:56 UTC (2,029 KB)
[v2] Sat, 27 Jul 2024 04:17:46 UTC (1,147 KB)
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