Set-theoretical decomposition on the basis of symmetric functions

Rytsar, B.

doi:10.1109/tcset.2018.8336334

Cited by 2 publications

(3 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, 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%

“…It is due to the fact that the basis of the known methods for recognizing of the types of symmetry is the analytical approach based on the Shannon expansion theorem [2,3,8] or a visual method based on the K-map [9,10]. Other known methods, such as the method of decomposition cloning on the basis of the q-partition conjuncterms procedure, in particular the BRASh algorithm [11], or a method based on the analytical calculation of logical derivatives, in particular the BOOLE algorithm (available over the Internet) [12,13]. These methods are somewhat simpler than mentioned, but require a preconversion of a given function.…”

Section: Introductionmentioning

confidence: 99%

“…The partial mixed symmetry recognition is demonstrated on the above example of the function (see Section 2) and, after its transformation -as perfect STF 1 1 {1, 2,6,7,8,11,12,13,16,19,20,21,25,26,30,31} Y = . This function has a pair of minterms (17), so firstly we will verify the condition (2) of the theorem.…”

mentioning

confidence: 96%

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

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

“…, 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 1 more Smart Citation

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

Set-theoretical decomposition on the basis of symmetric functions

Cited by 2 publications

References 5 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

Contact Info

Product

Resources

About