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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

2020

Vol. 117, iss. 1

art. no. e2020042

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.

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.

A comprehensive survey on formal concept analysis, its research trends and applications

Singh P. K., Aswani Kumar C., Gani A.

International Journal of Applied Mathematics and Computer Science

2016

Vol. 26, no. 2

495--516

In recent years, FCA has received significant attention from research communities of various fields. Further, the theory of FCA is being extended into different frontiers and augmented with other knowledge representation frameworks. In this backdrop, this paper aims to provide an understanding of the necessary mathematical background for each extension of FCA like FCA with granular computing, a fuzzy setting, interval-valued, possibility theory, triadic, factor concepts and handling incomplete data. Subsequently, the paper illustrates emerging trends for each extension with applications. To this end, we summarize more than 350 recent (published after 2011) research papers indexed in Google Scholar, IEEE Xplore, ScienceDirect, Scopus, SpringerLink, and a few authoritative fundamental papers.

On single-valued and multi-valued convergences

Bacher Ł., Kamiński A., Nalepa R.

Journal of Mathematics and Applications

2009

Vol. 31

19-27

We present a review of ideas of a general theory of convergence, developed independently of topology, with the stress on the duality of convergence and topology. Results and problems concerning sufficient and necessary conditions for a convergence to be topological, both in case of the single- and multi-valued cases, are recalled. We reconstruct, filling certain gaps, an example given in [7] to show that one of sufficient conditions in the theorems proved in [1] and [9] for multi-valued convergences to be topological is not necessary.