Is there an algebra of cellular automata?
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Algebraic cellular automata, which are cellular automata over groups with alphabets as affine algebraic sets and locally defined by regular maps, have been investigated in several papers. These automata have been shown to have a closed image with respect to the prodiscrete topology on the space of configurations when the ground field is uncountable and algebraically closed . Additionally, it has been proven that algebraic cellular automata are reversible as long as they are bijective . Furthermore, there is a study on elementary cellular automata from an algebraic viewpoint, aiming to relate the emergent complex behavior observed in such systems with the properties of corresponding algebraic structures . Another paper provides algebraic criteria for the unitarity of linear quantum cellular automata, both through combinatorial arguments and by adding constraints to the model . These papers collectively contribute to the understanding of the algebraic aspects of cellular automata.
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| Papers (5) | Insight |
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Open access•Posted Content | The paper does not explicitly mention an algebra of cellular automata. The paper focuses on providing algebraic criteria for the unitarity of linear quantum cellular automata. |
28 Aug 2006 9 Citations | The paper does not directly address the question of whether there is an algebra of cellular automata. The word "algebraic" is mentioned in the title and abstract, but it refers to algebraic criteria for the unitarity of linear quantum cellular automata, not a general algebra of cellular automata. |
11 Citations | The paper does not explicitly mention an "algebra of cellular automata." The paper discusses algebraic cellular automata and their properties, but does not specifically address the existence of an algebraic structure for cellular automata. |
| Yes, the paper discusses algebraic cellular automata as a generalization of elementary cellular automata, suggesting the existence of an algebraic structure for cellular automata. | |
| The paper does not explicitly mention an "algebra of cellular automata." The paper discusses algebraic cellular automata and their properties, but does not specifically address the existence of an algebraic structure for cellular automata. |
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