Nominal Cellular Automata
Tommaso Bolognesi (Istituto di Scienza e Tecnologie dell'Informazione, "A. Faedo", Consiglio Nazionale delle Ricerche), Vincenzo Ciancia (Istituto, di Scienza e Tecnologie dell'Informazione "A. Faedo", Consiglio Nazionale, delle Ricerche)
TL;DR
This paper explores Nominal Cellular Automata, a new computational model based on Nominal Sets, analyzing their behavior, computational power, and relation to classical cellular automata, with implications for physical phenomena modeling.
Contribution
It introduces Nominal Cellular Automata, examining their properties, computational capabilities, and connections to existing automata models, advancing the understanding of nominal computation in cellular automata.
Findings
Nominal Cellular Automata exhibit unique behavioral properties.
They have comparable computational capabilities to classical cellular automata.
Preliminary links to Wolfram's Elementary Cellular Automata are established.
Abstract
The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their computational capabilities, with a special focus on the emergent behavioural properties of this new model and their significance in the context of computation-oriented interpretations of physical phenomena. A preliminary investigation of the relations between Nominal Cellular Automata and Wolfram's Elementary Cellular Automata is also carried out.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Cellular Automata and Applications · semigroups and automata theory