On Shift Spaces with Algebraic Structure
Ville Salo, Ilkka T\"orm\"a
TL;DR
This paper explores algebraic subshifts, especially lattice-based ones, and studies cellular automata dynamics, providing characterizations and conditions for recoding into simpler forms.
Contribution
It offers new characterizations of Boolean algebraic subshifts and conditions for recoding algebraic subshifts into cellwise algebras, advancing understanding of their dynamics.
Findings
Characterization of Boolean algebraic subshifts
Conditions for recoding into cellwise algebras
Analysis of limit dynamics of homomorphic cellular automata
Abstract
We investigate subshifts with a general algebraic structure and cellular automata on them, with an emphasis on (order-theoretic) lattices. Our main results concern the characterization of Boolean algebraic subshifts, conditions for algebraic subshifts to be recoded into cellwise algebras and the limit dynamics of homomorphic cellular automata on lattice subshifts.
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Taxonomy
TopicsCellular Automata and Applications · semigroups and automata theory · Mathematical Dynamics and Fractals