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Mathematics > Dynamical Systems

arXiv:1609.09572 (math)
[Submitted on 30 Sep 2016 (v1), last revised 5 Apr 2017 (this version, v3)]

Title:Reversibility Problem of Multidimensional Finite Cellular Automata

Authors:Chih-Hung Chang, Hasan Akın
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Abstract:While the reversibility of multidimensional cellular automata is undecidable and there exists a criterion for determining if a multidimensional linear cellular automaton is reversible, there are only a few results about the reversibility problem of multidimensional linear cellular automata under boundary conditions. This work proposes a criterion for testing the reversibility of a multidimensional linear cellular automaton under null boundary condition and an algorithm for the computation of its reverse, if it exists. The investigation of the dynamical behavior of a multidimensional linear cellular automaton under null boundary condition is equivalent to elucidating the properties of block Toeplitz matrix. The proposed criterion significantly reduce the computational cost whenever the number of cells or the dimension is large; the discussion can also apply to cellular automata under periodic boundary condition with a minor modification.
Subjects: Dynamical Systems (math.DS); Information Theory (cs.IT)
Cite as: arXiv:1609.09572 [math.DS]
  (or arXiv:1609.09572v3 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1609.09572
Related DOI: https://doi.org/10.1007/s10955-017-1799-6

Submission history

From: Chih-Hung Chang Lucius [view email]
[v1] Fri, 30 Sep 2016 02:38:01 UTC (1,613 KB)
[v2] Tue, 10 Jan 2017 00:06:29 UTC (3,008 KB)
[v3] Wed, 5 Apr 2017 00:11:10 UTC (1,614 KB)
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