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 quasifair 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.

Dennunzio, A., Formenti, E., Manzoni, L., Mauri, G. (2013). m-Asynchronous Cellular Automata: from fairness to quasi-fairness. NATURAL COMPUTING, 12(4), 561-572 [10.1007/s11047-013-9386-5].

m-Asynchronous Cellular Automata: from fairness to quasi-fairness

DENNUNZIO, ALBERTO;MANZONI, LUCA;MAURI, GIANCARLO
2013

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 quasifair 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.
Articolo in rivista - Articolo scientifico
Cellular automata, Asynchronous cellular automata, Dynamical behavior, Decidability
English
2013
12
4
561
572
none
Dennunzio, A., Formenti, E., Manzoni, L., Mauri, G. (2013). m-Asynchronous Cellular Automata: from fairness to quasi-fairness. NATURAL COMPUTING, 12(4), 561-572 [10.1007/s11047-013-9386-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/43525
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