In this paper we define products of one-dimensional Number Conserving Cellular Automata (NCCA) and show that surjective NCCA with 2 blocks (i.e radius 1/2) can always be represented as products of shifts and identites. In particular, this shows that surjective 2-block NCCA are injective.
Volume: DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: Discrete dynamical systems,cellular automata,number conserving cellular automata,conservation laws,characterization of surjective NCCA,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS],[NLIN.NLIN-CG]Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
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3 Documents citing this article
Barbara Wolnik;Maciej Dziemiańczuk;Adam Dzedzej;Bernard De Baets, 2021, Reversibility of number-conserving 1D cellular automata: Unlocking insights into the dynamics for larger state sets, Physica D Nonlinear Phenomena, 429, pp. 133075, 10.1016/j.physd.2021.133075.
Katsunobu Imai;Bruno Martin;Ryohei Saito, Emergence, complexity and computation, On Radius 1 Nontrivial Reversible and Number-Conserving Cellular Automata, pp. 269-277, 2018, 10.1007/978-3-319-73216-9_12.