Additive Cellular Automata

Voorhees, Burton

doi:10.1007/978-1-4614-1800-9_1

Cited by 12 publications

(6 citation statements)

References 123 publications

(174 reference statements)

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“…CAs represent one of the simplest types of time, space, and value discrete dynamical systems and have been introduced initially by von Neumann [55,56]. Following this idea, CAs have been analyzed concerning several different properties, including structural [41,82], algebraic [18,31,49,77,79], dynamical [6,17,30,38,68], and behavioral [14,40,51,59,73] properties.…”

Section: Cellular Automatamentioning

confidence: 99%

“…( 4) have to be taken mod N . A subset of general CAs is given by Linear CAs [77]. The local rule of a linear CA is a Linear combination of the cell states in the considered neighborhood.…”

Section: Cellular Automatamentioning

confidence: 99%

“…. , w −1 ), (7) with circ as defined in [77] (note: if N = n, the circulant matrix has no additional zero entries that are not rule coefficients). Thus, the global rule for a Linear CA can be written as…”

Section: Cellular Automatamentioning

confidence: 99%

“…The global rule F of a Linear CA is surjective if every state configuration has a predecessor. Thus, surjective CAs have no GoE states and no transient phase [77]. Cattaneo et al [9] showed that transitive CAs are surjective.…”

Section: Surjectivity and Injectivitymentioning

confidence: 99%

“…Every injective CA is also surjective [46]. If F is surjective and injective, the CA is called bijective, which is equivalent to reversibility [77]. The condition for injectivity of a Linear CA is given by [31] (∀ p ∈ P)(∃ 1 w i ) :…”

Section: Surjectivity and Injectivitymentioning

confidence: 99%

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ReLiCADA: Reservoir Computing Using Linear Cellular Automata design algorithm

Kantic,

Legl,

Stechele

et al. 2024

Complex Intell. Syst.

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In this paper, we present a novel algorithm to optimize the design of Reservoir Computing using Cellular Automata models for time series applications. Besides selecting the models’ hyperparameters, the proposed algorithm particularly solves the open problem of Linear Cellular Automaton rule selection. The selection method pre-selects only a few promising candidate rules out of an exponentially growing rule space. When applied to relevant benchmark datasets, the selected rules achieve low errors, with the best rules being among the top 5% of the overall rule space. The algorithm was developed based on mathematical analysis of Linear Cellular Automaton properties and is backed by almost one million experiments, adding up to a computational runtime of nearly one year. Comparisons to other state-of-the-art time series models show that the proposed Reservoir Computing using Cellular Automata models have lower computational complexity and, at the same time, achieve lower errors. Hence, our approach reduces the time needed for training and hyperparameter optimization by up to several orders of magnitude.

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Section: Cellular Automatamentioning

confidence: 99%

“…( 4) have to be taken mod N . A subset of general CAs is given by Linear CAs [77]. The local rule of a linear CA is a Linear combination of the cell states in the considered neighborhood.…”

Section: Cellular Automatamentioning

confidence: 99%

Section: Cellular Automatamentioning

confidence: 99%

Section: Surjectivity and Injectivitymentioning

confidence: 99%