A Simple Numeric Set-Theoretical Method of the Logic Differential Calculus

Rytsar, B.

doi:10.15407/usim.2016.06.012

Cited by 2 publications

(4 citation statements)

References 6 publications

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“…In this paper we compared the calculation results of the proposed method with the decomposition cloning method and a BRASh program [16]. Here we demonstrate that the above-mentioned types of symmetries in boolean functions are easier to detect with the aid of a vectorial ST derivative of the 2nd order [15].…”

Section: The Basic Theoretical Partmentioning

confidence: 98%

“…It is known [15] that the vectorial ST-derivative of the 2-nd order with respect to arbitrary variables i x and j x of a function…”

Section: The Main Partmentioning

confidence: 99%

“…, we obtain the perfect STF 1 Y of the function f: (8,9,10,11,12,13,14,15), (4,5,6,7,12,13,14,15), }…”

Section: Recognition Of Partial Symmetries Types In Complete Functionsmentioning

confidence: 99%

“…In this paper we consider a new method for the recognition of symmetry in complete and incomplete functions on the basis of the author's proposed numerical set-theoretical definition of logical derivatives [15]. Compared with known methods, the proposed method algorithm differs by simpler practical implementation of the number of steps and the speed of detection and recognition of types of total and partial symmetries in complete and incomplete boolean functions and, as well as in the functions specified in SOP format, which is confirmed by numerous examples, borrowed from the publications of well-known authors.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A New Method for Symmetry Recognition in Boolean Functions Based on the Set-Theoretical Logic Differentiation. I

Rytsar¹,

Radioelectronics²

2019

Control syst. comput.

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The paper presents a new method for the recognition of the different types of total and partial symmetry in boolean functions based on the numeric set-theoretical differentiation. The proposed algorithm is based on the theorem on the recognition of different types of partial symmetry. This algorithm, compared to the known, has a relatively less computational complexity of realization due to a comparatively smaller number of operations and procedures necessary for the accomplishment of the given task. This is proved by the presented examples for the recognition of the proposed method of the different types of symmetry in complete and incomplete of Boolean functions, including given in the SOP format, taken for comparison reasons from publications of the wellknown authors.

show abstract

Section: The Basic Theoretical Partmentioning

confidence: 98%

“…It is known [15] that the vectorial ST-derivative of the 2-nd order with respect to arbitrary variables i x and j x of a function…”

Section: The Main Partmentioning

confidence: 99%

“…, we obtain the perfect STF 1 Y of the function f: (8,9,10,11,12,13,14,15), (4,5,6,7,12,13,14,15), }…”

Section: Recognition Of Partial Symmetries Types In Complete Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A New Method for Symmetry Recognition in Boolean Functions Based on the Set-Theoretical Logic Differentiation. I

Rytsar¹,

Radioelectronics²

2019

Control syst. comput.

View full text Add to dashboard Cite

show abstract

A New Method for Symmetry Recognition in Boolean Functions Based on the Set-Theoretical Logic Differentiation. II

Rytsar¹

2019

Control syst. comput.

View full text Add to dashboard Cite

The article describes a new method for the recognition of different types of total and partial symmetry in boolean functions based on the numeric set-theoretical differentiation. The proposed algorithm is based on the theorem on the recognition of different types of partial symmetry. This algorithm, compared to the known, has a relatively less computational complexity of realization due to a comparatively smaller number of operations and procedures necessary for the accomplishment of the given task. This is evidenced by the presented examples for the recognition of the proposed method of the different types of symmetry in complete and incomplete of Boolean functions, including given in the SOP format, borrowed for comparison reasons from publications of wellknown authors.

show abstract

A Simple Numeric Set-Theoretical Method of the Logic Differential Calculus

Cited by 2 publications

References 6 publications

A New Method for Symmetry Recognition in Boolean Functions Based on the Set-Theoretical Logic Differentiation. I

A New Method for Symmetry Recognition in Boolean Functions Based on the Set-Theoretical Logic Differentiation. I

A New Method for Symmetry Recognition in Boolean Functions Based on the Set-Theoretical Logic Differentiation. II

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