Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation
In this paper, a class of linear Boolean functions is analyzed. The Boolean function can be represented as disjoint cubes or in the form of a truth vector. The primary purpose of this analysis is to decide whether an incompletely defined function can be extended to a complete linear form. A simple a...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2022-12-01
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| Series: | Archives of Control Sciences |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/125428/PDF/1-Porwik_int.pdf |
| _version_ | 1797954376048836608 |
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| author | Piotr Porwik |
| author_facet | Piotr Porwik |
| author_sort | Piotr Porwik |
| collection | DOAJ |
| description | In this paper, a class of linear Boolean functions is analyzed. The Boolean function can be represented as disjoint cubes or in the form of a truth vector. The primary purpose of this analysis is to decide whether an incompletely defined function can be extended to a complete linear form. A simple algorithm for generating all states of this function has been proposed if the Boolean function can have a full representation. The algorithm is beneficial for large functions. The proposed approach can be applied to completely and incompletely defined Boolean functions. |
| first_indexed | 2024-04-10T23:17:40Z |
| format | Article |
| id | doaj.art-7870a574f0554502b41fd75c4090f70c |
| institution | Directory Open Access Journal |
| issn | 1230-2384 |
| language | English |
| last_indexed | 2024-04-10T23:17:40Z |
| publishDate | 2022-12-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Control Sciences |
| spelling | doaj.art-7870a574f0554502b41fd75c4090f70c2023-01-12T18:10:09ZengPolish Academy of SciencesArchives of Control Sciences1230-23842022-12-01vol. 32No 4663676https://doi.org/10.24425/acs.2022.143666Nonlinearity of incomplete Boolean functions: prioritizing spectra calculationPiotr Porwik0Faculty of Science and Technology, University of Silesia, Bedzinska 39, 41-200 Sosnowiec, PolandIn this paper, a class of linear Boolean functions is analyzed. The Boolean function can be represented as disjoint cubes or in the form of a truth vector. The primary purpose of this analysis is to decide whether an incompletely defined function can be extended to a complete linear form. A simple algorithm for generating all states of this function has been proposed if the Boolean function can have a full representation. The algorithm is beneficial for large functions. The proposed approach can be applied to completely and incompletely defined Boolean functions.https://journals.pan.pl/Content/125428/PDF/1-Porwik_int.pdfboolean functionnumerical methodswalsh transform |
| spellingShingle | Piotr Porwik Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation Archives of Control Sciences boolean function numerical methods walsh transform |
| title | Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation |
| title_full | Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation |
| title_fullStr | Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation |
| title_full_unstemmed | Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation |
| title_short | Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation |
| title_sort | nonlinearity of incomplete boolean functions prioritizing spectra calculation |
| topic | boolean function numerical methods walsh transform |
| url | https://journals.pan.pl/Content/125428/PDF/1-Porwik_int.pdf |
| work_keys_str_mv | AT piotrporwik nonlinearityofincompletebooleanfunctionsprioritizingspectracalculation |