The linear concept of logical synthesis of digital IP-modules of control and communication systems

Prokopenko, N. N.; Butyrlagin, N. V.; Chernov, N.I.; Yugai, Vladislav Ya.

doi:10.1109/sibcon.2015.7147182

Cited by 10 publications

(4 citation statements)

References 6 publications

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“…Three-valued logic can potentially produce considerable improvements in the field of computer networks and data networks. Research is in progress in the field of nonclassical approaches to logic synthesis and circuit design of digital IP modules for computer technology, and control and communication systems [38,41,42,57].…”

Section: Discussionmentioning

confidence: 99%

“…A similar process of the logical synthesis and circuit design of double-and multivalued digital nodes was described in [57], demonstrating the advantages of the considered architectural and circuitry solutions for the synthesis of double-and multivalued digital nodes of different applications in comparison to double-valued Boolean algebra. However, these results describe the concept rather than providing a method of synthesizing circuits from a practical point of view.…”

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confidence: 82%

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Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

Kalimulina

2021

Mathematics

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This paper provides a brief overview of modern applications of nonbinary logic models, where the design of heterogeneous computing systems with small computing units based on three-valued logic produces a mathematically better and more effective solution compared to binary models. For application, it is necessary to implement circuits composed of chipsets, the operation of which is based on three-valued logic. To be able to implement such schemes, a fundamentally important theoretical problem must be solved: the problem of completeness of classes of functions of three-valued logic. From a practical point of view, the completeness of the class of such functions ensures that circuits with the desired operations can be produced from an arbitrary (finite) set of chipsets. In this paper, the closure operator on the set of functions of three-valued logic that strengthens the usual substitution operator is considered. It is shown that it is possible to recover the sublattice of closed classes in the general case of closure of functions with respect to the classical superposition operator. The problem of the lattice of closed classes for the class of functions T2 preserving two is considered. The closure operators R1 for the functions that differ only by dummy variables are considered equivalent. This operator is withiin the scope of interest of this paper. A lattice is constructed for closed subclasses in T2={f|f(2,…,2)=2}, a class of functions preserving two.

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 82%

Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

Kalimulina

2021

Mathematics

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“…In accordance with [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], the synthesis of the functional scheme corresponding to any logic function consists in multiplying the row-vector of the values of the function by the inverse basic matrix and obtaining the expansion vector of the function from the selected basis, and then recording the representation of the function as a weighted sum of the basis vectors. We perform the synthesis of the selected schemes using the basis presented below.…”

Section: Logic Elements and Or Notmentioning

confidence: 94%

“…The authors published a number of papers [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] devoted to the synthesis of logic (nonthreshold) two-valued and multivalued digital structures. This paper considers the use of linear algebra as a mathematical tool for the logic synthesis of two-valued and multivalued, logic and threshold digital structures.…”

Section: Introductionmentioning

confidence: 99%

Linear algebra as an alternative approach to the synthesis of digital devices of automation and control systems

Chernov¹,

Prokopenko²,

Yugai³

et al. 2018

Adv. sci. technol. eng. syst. j.

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The article considers linear algebra as an alternative mathematical tool of logic synthesis of digital structures to Boolean algebra and synthesis methods of digital electronic component base (ECB) on its ground. The methods of solving the applied problems of logic synthesis are shown, including the expansion of an arbitrary logic function by means of monotonic functions. The proposed mathematical apparatus actually provides the creation of digital structures on the principles of analog circuitry. It can find application in

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CMOS Current Logic Elements: Application Features for Processing Analog and Digital Signals

Butyrlagin

Chernov

Prokopenko

et al. 2018

2018 XIV International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE)

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The linear concept of logical synthesis of digital IP-modules of control and communication systems

Cited by 10 publications

References 6 publications

Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

Linear algebra as an alternative approach to the synthesis of digital devices of automation and control systems

CMOS Current Logic Elements: Application Features for Processing Analog and Digital Signals

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