arXiv subjects

Alexander Yu. Chunikhin

Publications and source records attributed to Alexander Yu. Chunikhin.

5 recordsLinked to original sources

arXiv2025

Semantic Numeration Systems as Dynamical Systems

The foundational concepts of semantic numeration systems theory are briefly outlined. The action of cardinal semantic operators unfolds over a set of cardinal abstract entities belonging to the cardinal semantic multeity. The cardinal abstract object (CAO) formed by them in a certain connectivity topology is proposed to be considered as a linear discrete dynamical system with nonlinear control. Under the assumption of ideal observability, the CAO state equations are provided for both stationary and non-stationary cases. The fundamental role of the configuration matrix, which combines information about the types of cardinal semantic operators in the CAO, their parameters and topology of connectivity, is demonstrated.

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arXiv2024

CHTW-systems with resource-depended parameters. CHTW(R)-systems

In [1] the concept of CHTW-systems as a multidimensional representation of Petri nets was proposed based on the assumption of multidimensional distribution of tokens (resources) in positions (branes) and, accordingly, multidimensional representation of transitions and arcs. The extension of Petri nets was developed under the assumption of the stationarity of CHTW-system, when its parameters are constant during the system operation. We consider the case when the main parameters of CHTW-system (threshold functions and rate functions) change in accordance with the values of the mark-functions (multidimensional resource) of some container branes of the same CHTW-system. The modification of the basic CHTW-system was designated as a CHTW(R) system, in which (R) means a Resource control of the system parameters.

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arXiv2023

Theory of CHTW-systems. Born by Petri Nets

For the first time, the concept of CHTW-systems as a multidimensional representation of Petri nets, based on the assumption of the spatial distribution of tokens (resources) in positions (branes) and, accordingly, the spatial representation of transitions and arcs is proposed. The theoretical constructs are based on the concept of hybrid functional Petri nets [10]. The introduced concepts of branes and carriers are distant analogies of the corresponding concepts in superstring theory, but the theory of CHTW-systems is neither part of superstring theory nor its development. The description of CHTW-system as a dynamic system for stationary and non-stationary cases is considered. The initial classification of CHTW systems is provided enabling understanding of further research directions.

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arXiv2019

On Concept of Petri Nets Receptors and Effectors

New subclasses of Petri nets - Petri nets receptors and Petri nets effectors are introduced. The introduction/exclusion of such substructures in the main Petri net may be fulfilled in accordance with the Fusion/Defusion principles. We propose two pairs of entities: position marking receptor (effector) and transition marking receptor (effector), which allow to observe parameters of the main Petri net and, if necessary, to carry out their regulation.

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arXiv2019

On Concept of Creative Petri Nets

A new formalism of Petri nets, based on the adoption of the "position-arc-transition" triad and "transition-arc-position" triad as structure-forming units is introduced. In accordance with the Fusion principle, an analytical representation of Petri nets is developed. We propose the concept of Creative Petri Nets, which allows to implement structural changes in Petri net by procreation/deletion of structural units or complexes.

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