Classification of Faults in Cyber-Physical Systems with Complex-Valued Neural Networks

Pfeifer, Anton; Lohweg, Volker

doi:10.1109/etfa45728.2021.9613451

Cited by 1 publication

(1 citation statement)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, k-valued logic is highly relevant in the modeling of complex dynamical systems, where causal relations play a crucial role [4]. It is also used in logical dynamical systems [5], the modern control and stabilization of unmanned systems [6], cyber-physical systems [7], data transmission [8,9], optimal network routing [10,11], and quantum cryptography [12]. A comprehensive analysis of the use of k-valued logic in various applications has been provided in the research paper [9].…”

Section: Introductionmentioning

confidence: 99%

Finiteness of One-Valued Function Classes in Many-Valued Logic

Kalimulina

2023

Fractal Fract

View full text Add to dashboard Cite

This paper addresses the theoretical issues in k-valued logic, which are crucial for developing solutions in various fields of science and technology. One of the fundamental issues is a complete description of the closed classes of functions of three-valued logic. The explicit description of closed classes in multivalued logic is an open problem. In this study, we consider a special case of the finite generation of all closed classes of three-valued logic through the operation of superposition. Previously, we considered the issue of the finite generation of classes containing a subset of single-variable functions. We have also provided a description of superlattices (lattices of lattices) containing a precomplete class of unary functions. The finite generation of these superlattices is proved. On the basis of these results, in this paper, we have proven that any class containing any of the precomplete classes from the set of single-valued functions is also finitely generated. The main result of this paper consists of three theorems on the finite generation of classes containing precomplete classes of single-valued functions and classes including all monotone unary functions. Thus, the obtained theoretical result provides easily verifiable criteria for the finiteness of classes of multivalued logic functions. It allows you to use simple procedures instead of cumbersome explicit constructs. The finite generation of overlattices allows the development of digital computing circuits that are crucial for practical applications. The proofs are based on an explicit description of these classes by an induction in the number of variables and essentially use the properties of functionally closed (Burle) classes of functions.

show abstract

Section: Introductionmentioning

confidence: 99%

Finiteness of One-Valued Function Classes in Many-Valued Logic

Kalimulina

2023

Fractal Fract

View full text Add to dashboard Cite

show abstract

Classification of Faults in Cyber-Physical Systems with Complex-Valued Neural Networks

Cited by 1 publication

References 18 publications

Finiteness of One-Valued Function Classes in Many-Valued Logic

Finiteness of One-Valued Function Classes in Many-Valued Logic

Contact Info

Product

Resources

About