Natural Computing

, Volume 12, Issue 4, pp 561–572

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

  • Alberto Dennunzio
  • Enrico Formenti
  • Luca Manzoni
  • Giancarlo Mauri
Article

DOI: 10.1007/s11047-013-9386-5

Cite this article as:
Dennunzio, A., Formenti, E., Manzoni, L. et al. Nat Comput (2013) 12: 561. doi:10.1007/s11047-013-9386-5

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.

Keywords

Cellular automata Asynchronous cellular automata Dynamical behavior Decidability 

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Alberto Dennunzio
    • 1
  • Enrico Formenti
    • 2
  • Luca Manzoni
    • 2
  • Giancarlo Mauri
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanItaly
  2. 2.Laboratoire I3SUniversité Nice Sophia AntipolisSophia AntipolisFrance