BIJECTIVE COORDINATE-FORBIDDEN k-VALUED FUNCTIONS IN A PROBLEM OF SYNTHESIS OF SUBSTITUTIONS
( Pp. 14-23)
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Churov Dmitry Valeryevich
sotrudnik FGUP «NII «KVANT»
Federal State Unitary Enterprise Scientific Research Institute KVANT Nikonov Vladimir G. Doctor of Engineering, Professor; member at the Presidium
Russian Academy of Natural Sciences
Moscow, Russian Federation
Federal State Unitary Enterprise Scientific Research Institute KVANT Nikonov Vladimir G. Doctor of Engineering, Professor; member at the Presidium
Russian Academy of Natural Sciences
Moscow, Russian Federation
Abstract:
The interest towards the study of transformations in a k-valued logic is driven to a great extent by the development of modern computer technology, particularly by the increase in the amount of information and the increasing speed of information processing. The transition from Boolean operations to k-valued operations is not limited to a quantitative increase in complexity, as it also affects the internal logical framework of the schemes' implementation and functioning. This article will focus on the study of a specific locally defined problem of k-valued logic, namely, the problem of expansive interpretation of the logical negation operation, which, despite the simplicity of its original definition, has led to the creation of a theory of functions with forbidden signs of subfunctions. Of additional interest are original practical applications of this theory associated with the study of a range of typical information processing nodes using functions of the studied class.
How to Cite:
Churov D.V., Nikonov V.G., (2016), BIJECTIVE COORDINATE-FORBIDDEN K-VALUED FUNCTIONS IN A PROBLEM OF SYNTHESIS OF SUBSTITUTIONS. Computational Nanotechnology, 1 => 14-23.
Reference list:
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Fomichyev V.M. Diskretnaya matematika i kriptologiya. -Moskva: Dialog-MIFI , 2003.
Glukhov M.M., Elizarov V.P., Nechaev A.A. Algebra. 2003. T. 1, 2.
Alfyerov A.P., Zubov A.YU., Kuz min A.S., CHeryemushkin A.V. Osnovy kriptografii. -Moskva: Gelios ARV, 2005.
Glukhov M.M., SHishkov A.B. Matematicheskaya logika. Diskretnye funktsii. Teoriya algoritmov. SPb. -M. -Krasnodar: Lan , 2012.
Fomichyev V.M. Diskretnaya matematika i kriptologiya. -Moskva: Dialog-MIFI , 2003.
Glukhov M.M., Elizarov V.P., Nechaev A.A. Algebra. 2003. T. 1, 2.
Alfyerov A.P., Zubov A.YU., Kuz min A.S., CHeryemushkin A.V. Osnovy kriptografii. -Moskva: Gelios ARV, 2005.
Glukhov M.M., SHishkov A.B. Matematicheskaya logika. Diskretnye funktsii. Teoriya algoritmov. SPb. -M. -Krasnodar: Lan , 2012.
Keywords:
bijective mapping, k-valued functions with forbidden signs subfunctions.
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