Cellular Automata with Anticipation: Examples and Presumable Applications

Krushinsky, Dmitry; Makarenko, Alexander

doi:10.1063/1.3527160

Cited by 13 publications

(13 citation statements)

References 8 publications

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“…Such descriptions and illustrations are need for understanding the discussion in the section 5. More details are described in our publications [19,20].…”

Section: Game 'Life' With Strong Anticipationmentioning

confidence: 99%

“…To endow a model with anticipation property one has to design a next step function that depends on the next (expected, virtual) cell states [19,20]. Many possibilities exist to implement it.…”

Section: Cells With Anticipationmentioning

confidence: 99%

“…Many possibilities exist to implement it. We took in [19,20] as the illustrative example for CA with anticipation the case when the next state function of classical "Life" defined as:…”

Section: Cells With Anticipationmentioning

confidence: 99%

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Multivaluedness in Cellular Automata with Strong Anticipation and Some Prospects for Computation Theory

Makarenko¹

2020

Wseas Transactions on Information Science and Applications

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It is considered the general formulations and properties of cellular automata with cells which have the strong anticipatory property (introduced by D. Dubois). Multivalued behavior (hyperincursion) of solutions of such CA is described. It was posed new research problems of computation theory related to presumable multivaluedness of cellular automata with strong anticipation property. Extending of classical automata, Turing machine and algorithms had been proposed. Also some relation of such cellular automata and quantum mechanics are discussed.

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“…Such descriptions and illustrations are need for understanding the discussion in the section 5. More details are described in our publications [19,20].…”

Section: Game 'Life' With Strong Anticipationmentioning

confidence: 99%

Section: Cells With Anticipationmentioning

confidence: 99%

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Multivaluedness in Cellular Automata with Strong Anticipation and Some Prospects for Computation Theory

Makarenko¹

2020

Wseas Transactions on Information Science and Applications

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“…Note that all the development of cellular automata occurred approximately as follows -there were certain concepts (such as classical or quantum computing) that then were embedded into the concept of cellular automata. Of course, the proposed cellular automata with anticipation [8] partially admit such an immersion into existing classical concepts. We call it the direct way of theory development.…”

Section: Presumable Development Of the Theory Of Cellular Automatamentioning

confidence: 99%

“…Some features of cellular automata with strong anticipation are described in [8]. We stress here only some interesting features.…”

Section: Problem Of the Reconstruction Of Conceptsmentioning

confidence: 99%

Recent Advances in Nonlinear Dynamics and Synchronization

2018

Studies in Systems, Decision and Control

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Since the introduction of strong anticipation by D. Dubois the numerous investigations of concrete systems have been proposed. In proposed paper the new examples of discrete dynamical systems with anticipation are considered. The mathematical formulation of problems, possible analytical formulas for solutions and numerical examples of presumable solutions are proposed. One of the most interesting properties in such systems is presumable multivaluedness of the solutions. It can be considered from the point of view of dynamical chaos and complex behavior. We represent examples of periodic and complex solutions, attractor's properties and presumable applications in self-organization. The main peculiarity is the strong anticipation property. General new possibilities are the presumable multivaluedness of the dynamics of automata. Possible interpretations of such behavior of cellular automata are discussed. Further prospects for development of automata theory and hyper computation are proposed.

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Presumable Applications of Deep Learning for Cellular Automata Identification

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Makarenko

2019

Proceedings of the International Neural Networks Society

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Cellular Automata with Anticipation: Examples and Presumable Applications

Cited by 13 publications

References 8 publications

Multivaluedness in Cellular Automata with Strong Anticipation and Some Prospects for Computation Theory

Multivaluedness in Cellular Automata with Strong Anticipation and Some Prospects for Computation Theory

Recent Advances in Nonlinear Dynamics and Synchronization

Presumable Applications of Deep Learning for Cellular Automata Identification

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