The Computation for Reversibility of Arbitrary One-dimensional Finite Cellular Automata Becomes Efficient

Author:

Chen Wang, Junchi Ma, Chao Wang, Defu Lin, Weilin Chen

Keyword:

Nonlinear Sciences, Cellular Automata and Lattice Gases, Cellular Automata and Lattice Gases (nlin.CG), Computational Complexity (cs.CC)

journal:

date:

2024-02-08 00:00:00

Abstract

In this paper, we completely solve the reversibility of one-dimensional finite cellular automata (FCA). This means that we will have an efficient method to determine the reversibility of any FCA with all numbers (n) of cells. The complexity of this algorithm is independent of n. We perform calculations on two new kinds of graphs and discover that the reversibility of any FCA exhibits periodicity as n increases. We successfully provide a method to compute the reversibility sequence that encompasses the reversibility of FCA with any number of cells. Additionally, the calculations in this paper are applicable to FCA with various types of boundaries.

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