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Nonlinear Sciences > Cellular Automata and Lattice Gases

arXiv:nlin/0306032 (nlin)
[Submitted on 17 Jun 2003]

Title:Universality and Decidability of Number-Conserving Cellular Automata

Authors:Andres Moreira
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Abstract: Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the definition of the property to include cellular automata with any set of states in $\Zset$, and show that they can be always extended to ``usual'' NCCA with contiguous states. We show a way to simulate any one dimensional CA through a one dimensional NCCA, proving the existence of intrinsically universal NCCA. Finally, we give an algorithm to decide, given a CA, if its states can be labeled with integers to produce a NCCA, and to find this relabeling if the answer is positive.
Comments: 13 pages
Subjects: Cellular Automata and Lattice Gases (nlin.CG)
Cite as: arXiv:nlin/0306032 [nlin.CG]
  (or arXiv:nlin/0306032v1 [nlin.CG] for this version)
  https://doi.org/10.48550/arXiv.nlin/0306032
Journal reference: Final version published in Theoretical Computer Science, 292:711--721 (2003)

Submission history

From: Andres Moreira [view email]
[v1] Tue, 17 Jun 2003 21:37:46 UTC (12 KB)
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