Multi-Resolution Cellular Automata for Real Computation

Lathrop, James I.; Lutz, Jack H.; Patterson, Brian

doi:10.1007/978-3-642-21875-0_19

Cited by 3 publications

(4 citation statements)

References 17 publications

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“…There are many, more specific-purpose models which a posteriori can be viewed as instances of the notion of causal graph dynamics developed in this paper [19,28,25,27]. We now show via two examples that our model subsumes, but is not restricted to, Cellular Automata.…”

Section: Examples Of Localizable Dynamicsmentioning

confidence: 87%

Causal Graph Dynamics

Arrighi

Dowek

2012

Automata, Languages, and Programming

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Section: Examples Of Localizable Dynamicsmentioning

confidence: 87%

Causal Graph Dynamics

Arrighi

Dowek

2012

Automata, Languages, and Programming

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“…There are many, more specific-purpose models which a posteriori can be viewed as instances of the notion of causal graph dynamics developed in this paper [20,29,26,28]. We now show via two examples that our model subsumes, but is not restricted to, cellular automata.…”

Section: Examples Of Localisable Functionsmentioning

confidence: 87%

“…This inflating grid may also be viewed as a way to generate smaller and smaller structures in a fixed size system, as in [26].…”

Section: Proofmentioning

confidence: 99%

Causal graph dynamics

Arrighi

Dowek

2013

Information and Computation

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International audienceWe extend the theory of cellular automata to arbitrary, time-varying graphs. In other words we formalise, and prove theorems about, the intuitive idea of a labelled graph which evolves in time -- but under the natural constraint that information can only ever be transmitted at a bounded speed, with respect to the distance given by the graph. The notion of translation-invariance is also generalised. The definition we provide for these 'causal graph dynamics' is simple and axiomatic. The theorems we provide also show that it is robust. For instance, causal graph dynamics are stable under composition and under restriction to radius one. In the finite case some fundamental facts of cellular automata theory carry through: causal graph dynamics admit a characterisation as continuous functions, and they are stable under inversion. The provided examples suggest a wide range of applications of this mathematical object, from complex systems science to theoretical physics

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“…In Chapter 3, we examine how the multi-resolution cellular automaton (MRCA) provides a new approach to understanding the field of computable analysis. This chapter is based on work with Lathrop and Lutz [28].…”

Section: Multi-resolution Cellular Automata and Computable Analysismentioning

confidence: 99%

Three topics in the theory of computing: Multi-resolution cellular automata, the Kolmogorov complexity characterization of regular languages, and hidden variables in Bayesian networks

Patterson

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Multi-Resolution Cellular Automata for Real Computation

Cited by 3 publications

References 17 publications

Causal Graph Dynamics

Causal Graph Dynamics

Causal graph dynamics

Three topics in the theory of computing: Multi-resolution cellular automata, the Kolmogorov complexity characterization of regular languages, and hidden variables in Bayesian networks

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