1,515 research outputs found
On injective endomorphisms of symbolic schemes
Building on the seminal work of Gromov on endomorphisms of symbolic algebraic
varieties [10], we introduce a notion of cellular automata over schemes which
generalize affine algebraic cellular automata in [7]. We extend known results
to this more general setting. We also establish several new ones regarding the
closed image property, surjunctivity, reversibility, and invertibility for
cellular automata over algebraic varieties with coefficients in an
algebraically closed field. As a byproduct, we obtain a negative answer to a
question raised in [7] on the existence of a bijective complex affine algebraic
cellular automaton whose inverse
is not algebraic
Translating partitioned cellular automata into classical type cellular automata
ISBN 978-5-94057-377-7International audiencePartitioned cellular automata are a variant of cellular automata that was defined in order to make it very simple to create complex automata having strong properties such as number conservation and reversibility (which are often difficult to obtain on cellular automata). In this article we show how a partitioned cellular automaton can be translated into a regular cellular automaton in such a way that these properties are conserved
The reversibility of cellular automata on trees with loops
[EN] In this work the notion of linear cellular automata on trees with loops is introduced and the reversibility problem in some particular cases is tackled. The explicit expressions of the inverse cellular automata are computed
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