Neural Networks with Strong Anticipation and Some Related Problems of Complexity Theory

Makarenko, O. S.

doi:10.1007/978-3-319-28860-4_12

Cited by 4 publications

(5 citation statements)

References 10 publications

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“…У 1992 р. Д. Дюбуа [7][8][9] запропонував поняття інкурсії, антисипації або передбачення, коли новий стан об'єкта залежить не тільки від певних попередніх станів, а і від певних майбутніх станів (сильна антисипація) або їх оцінок (слабка антисипація). Об'єкти можуть бути різної природи: диференціальні рівняння з неперервним часом та їх скінченно-різницеві аналоги з дискретним часом, диференціальні рівняння звичайні та з частинними похідними, клітинні автомати досліджувались, наприклад, у працях [7][8][9][10][11][12], диференціальні рівняння з випереджальним аргументом -у працях [13][14][15].…”

Section: вступunclassified

A modification of Petri nets with anticipation on a position

Statkevych¹

2023

SRIT

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We propose a modification of Petri nets with strong anticipation on a position. The extension modifies a transition rule by adding a new term that contains an integer function of the new marking in the position. The differences from classic Petri nets are found; for example, the set of markings that are reachable from a current marking by firing the enabled transition can either be empty or contain more than one marking. We consider the construction of a reachability graph and a coverability tree. We give the conditions for the existence of the coverability tree and propose the algorithm for constructing the coverability tree that generalizes the well-known classic algorithm. The main ideas and constructions are illustrated in the examples.

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Section: вступunclassified

A modification of Petri nets with anticipation on a position

Statkevych¹

2023

SRIT

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“…Other very important object of proposed type (with anticipation and discrete time dynamic) is neural networks with strong anticipation. We have already investigated some such models [12]. Here we propose only very short description of calculations for understanding of presumable behavior.…”

Section: Neural Network With Anticipationmentioning

confidence: 99%

“…The first is two-steps nature (that is passing on two steps ahead at discrete). The second is that the function f (x) in the model has a piecewise-linear character, and looks like the transition function of neurons in neuronets [12]. Remark that the piecewise character of the nonlinearity usually allows to simplify mathematical investigations.…”

Section: Two-steps Discrete-time Anticipatory Modelsmentioning

confidence: 99%

“…One of the most important examples of the models with anticipation follows from modeling of large social systems. Some examples of investigations of the systems with strong anticipation were described in [9]- [12], [15]- [18]. Remark that one of the most new and interesting properties in such systems is presumable multivaluednes of the solutions.…”

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confidence: 99%

“…But recently it has been found that the investigation of the systems with anticipation is also very interesting. The term 'anticipation' was firstly attached to the systems with the intrinsic models for predicting the evolution of the systems and of their environment (see [17], [4,5], [9]- [12], [15]- [18] and many others). But now since the works by Daniel M. Dubois (Belgium) the notion of 'strong anticipation' has been introduced and investigated.…”

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confidence: 99%

See 2 more Smart Citations

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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Multiple-Valued Neural Networks and Branching Neural Networks

Makarenko

2022

Complex Systems: Spanning Control and Computational Cybernetics: Foundations

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Neural Networks with Strong Anticipation and Some Related Problems of Complexity Theory

Cited by 4 publications

References 10 publications

A modification of Petri nets with anticipation on a position

A modification of Petri nets with anticipation on a position

Recent Advances in Nonlinear Dynamics and Synchronization

Multiple-Valued Neural Networks and Branching Neural Networks

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