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Construction of Generalized Rademacher Functions in Terms of Ternary Logic : Solving the Problem of Visibility of Using Galois Fields for Digital Signal Processing

Vitulyova Elizaveta S., Matrassulova Dinara K., Suleimenov Ibragim E.

International Journal of Electronics and Telecommunications

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2022

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Vol. 68, No. 2

237--244

EN

Generalized Rademacher functions, constructed as a sequence of elements of Galois fields are intended to find the spectral representation of signals with levels. These functions form a complete basis on the interval corresponding to -1 discrete time intervals and for passing into the classical Rademacher functions. The advantage of such spectra obtained using Galois Fields Fourier Transform is that the range of variation of the spectrum amplitudes remains the same as the range of variation of the original signal, which is modeled on discrete time functions taking values in the Galois field.

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An explanation of the Landauer bound and its ineffectiveness with regard to multivalued logic

Kycia Radosław A., Niemczynowcz Agnieszka

Technical Transactions

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2020

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Vol. 117, iss. 1

art. no. e2020042

EN

We discuss, using recent results on the thermodynamics of multivalued logic, the difficulties and pitfalls of how to apply the Landauer’s principle to thermodynamic computer memory models. The presentation is based on Szilard’s version of Maxwell’s demon experiment and use of equilibrium Thermodynamics. Different versions of thermodynamic/mechanical memory are presented – a one-hot encoding version and an implementation based on a reversed Szilard’s experiment. The relationship of the Landauer’s principle to the Galois connection is explained in detail.

PL

Opisujemy, używając niedawne badania związane z termodynamiką dla logiki wielowartościowej, problemy związane z zastosowaniem reguły Landauera dla termodynamicznego modelu pamięci komputera. Analiza jest oparta na wersji Szilarda demona Maxwella z termodynamiki równowagowej. Zostały zaprezentowane różne wersje termodynamicznej/mechanicznej pamięci – wersja gorąco jedynkowa i implementacja bazująca na odwróconym eksperymencie Szilarda. Zaprezentowano również związek pomiędzy regułą Landauera i koneksją Galois.

3

On Designated Values in Multi-Valued CTLS* Model Checking

Konikowska B., Penczek W.

Fundamenta Informaticae

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2004

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Vol. 60, nr 1-4

211--224

EN

A multi-valued version of CTLS* (mv-CTLS*), where both the propositions and the accessibility relation are multi-valued, taking values in a complete lattice with a complement, is considered. Contrary to all the existing model checking results for multi-valued modal logics, our lattices are not required to be finite. A set of restrictions is provided under which there is a direct translation from mv-CTLS* to CTLS* model checking problem for designated values. Bisimulation induced by mv-CTLS* is characterized.

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Sensor, Filter, and Fusion Models with Rough Petri Nets

Peters J.F., Ramanna S., Borkowski M., Skowron A., Suraj Z.

Fundamenta Informaticae

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2001

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Vol. 47, nr 3,4

307-323

EN

This paper considers models of sensors, filters, and sensor fusion with Petri nets defined in the context of rough sets. Sensors and filters are fundamental computational units in the design of systems. The intent of this work is to construct Petri nets to simulate conditional computation in approximate reasoning systems, which are dependent on filtered input from selected sensors considered relevant in problem solving. In this paper, coloured Petri nets provide a computational framework for the definition of a family of Petri nets based on rough set theory. Sensors are modeled with what are known as receptor processes in rough Petri nets. Filters are modeled as ukasiewicz guards on some transitions in rough Petri nets. A ukasiewicz guard is defined in the context of multivalued logic. ukasiewicz guards are useful in culling from a collection of active sensors those sensors with the greatest relevance in a problem-solving effort such as classification of a "perceived" phenomenon in the environment of an agent. The relevance of a sensor is computed using a discrete rough integral. The form of sensor fusion considered in this paper consists in selecting only those sensors considered relevant in solving a problem. The contribution of this paper is the modeling of sensors, filters, and fusion in the context of receptor processes, ukasiewicz guards, and rough integration, respectively.