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m-Asynchronous cellular automata: from fairness to quasi-fairness

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Abstract

A new model for the study of asynchronous cellular automata dynamical behavior is introduced with the main purpose of unifying several existing paradigms. The main idea is to measure the set of updating sequences to quantify the dependency of the properties under investigation from them. We propose to use the class of quasi-fair measures, namely measures that satisfy some fairness conditions on the updating sequences. Basic set properties like injectivity and surjectivity are adapted to the new setting and studied. In particular, we prove that they are dimensions sensitive properties (i.e., they are decidable in dimension 1 and undecidable in higher dimensions). A first exploration of dynamical properties is also started, some results about equicontinuity and expansivity behaviors are provided.

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Acknowledgments

This work has been partially supported by the French National Research Agency project EMC (ANR-09-BLAN-0164) and by the Italian PRIN 2010-2011/MIUR project “Automata and Formal Languages: Mathematical and Applicative Aspects”.

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Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, viale Sarca 336, 20126, Milan, Italy

    Alberto Dennunzio & Giancarlo Mauri

  2. Laboratoire I3S, Université Nice Sophia Antipolis, 2000 Route des Colles, 06903, Sophia Antipolis, France

    Enrico Formenti & Luca Manzoni

Authors
  1. Alberto Dennunzio
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  2. Enrico Formenti
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  3. Luca Manzoni
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  4. Giancarlo Mauri
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Correspondence to Alberto Dennunzio.

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Dennunzio, A., Formenti, E., Manzoni, L. et al. m-Asynchronous cellular automata: from fairness to quasi-fairness. Nat Comput 12, 561–572 (2013). https://doi.org/10.1007/s11047-013-9386-5

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