Atomic Formulation of the Boolean Curve Fitting Problem
Boolean curve fitting is the process of finding a Boolean function that takes given values at certain points in its Boolean domain. The problem boils down to solving a set of ‘big’ Boolean equations that may or may not be consistent. The usual formulation of the Boolean curve fitting problem is quit...
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| Format: | Article |
| Language: | English |
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Ram Arti Publishers
2022-10-01
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| Series: | International Journal of Mathematical, Engineering and Management Sciences |
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| Online Access: | https://ijmems.in/cms/storage/app/public/uploads/volumes/44-IJMEMS-22-0138-7-5-670-680-2022.pdf |
| _version_ | 1818029446061359104 |
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| author | Ahmed S. Balamesh Ali M. Rushdi |
| author_facet | Ahmed S. Balamesh Ali M. Rushdi |
| author_sort | Ahmed S. Balamesh |
| collection | DOAJ |
| description | Boolean curve fitting is the process of finding a Boolean function that takes given values at certain points in its Boolean domain. The problem boils down to solving a set of ‘big’ Boolean equations that may or may not be consistent. The usual formulation of the Boolean curve fitting problem is quite complicated, indeed. In this paper, we formulate the Boolean curve fitting problem using the technique of atomic decomposition of Boolean equations. This converts the problem into a set of independent switching equations. We present the solution of these switching equations and express the solution in very simple and compact forms. We also present the consistency and uniqueness conditions for this problem again in very compact forms. A few illustrative examples are given. These examples clearly pinpoint the simplicity gained by the Boolean-equation solving step within the overall Boolean-fitting procedure. The method presented here can be applied to the design of Boolean functions for cryptographic systems. |
| first_indexed | 2024-12-10T05:19:49Z |
| format | Article |
| id | doaj.art-eb13342586fa43e1966cd17d3630e6df |
| institution | Directory Open Access Journal |
| issn | 2455-7749 |
| language | English |
| last_indexed | 2024-12-10T05:19:49Z |
| publishDate | 2022-10-01 |
| publisher | Ram Arti Publishers |
| record_format | Article |
| series | International Journal of Mathematical, Engineering and Management Sciences |
| spelling | doaj.art-eb13342586fa43e1966cd17d3630e6df2022-12-22T02:00:51ZengRam Arti PublishersInternational Journal of Mathematical, Engineering and Management Sciences2455-77492022-10-0175670680https://doi.org/10.33889/IJMEMS.2022.7.5.044Atomic Formulation of the Boolean Curve Fitting ProblemAhmed S. Balamesh0Ali M. Rushdi1Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah, Saudi Arabia.Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah, Saudi Arabia.Boolean curve fitting is the process of finding a Boolean function that takes given values at certain points in its Boolean domain. The problem boils down to solving a set of ‘big’ Boolean equations that may or may not be consistent. The usual formulation of the Boolean curve fitting problem is quite complicated, indeed. In this paper, we formulate the Boolean curve fitting problem using the technique of atomic decomposition of Boolean equations. This converts the problem into a set of independent switching equations. We present the solution of these switching equations and express the solution in very simple and compact forms. We also present the consistency and uniqueness conditions for this problem again in very compact forms. A few illustrative examples are given. These examples clearly pinpoint the simplicity gained by the Boolean-equation solving step within the overall Boolean-fitting procedure. The method presented here can be applied to the design of Boolean functions for cryptographic systems.https://ijmems.in/cms/storage/app/public/uploads/volumes/44-IJMEMS-22-0138-7-5-670-680-2022.pdfboolean curve fittingboolean equationsatomic decompositioncryptography |
| spellingShingle | Ahmed S. Balamesh Ali M. Rushdi Atomic Formulation of the Boolean Curve Fitting Problem International Journal of Mathematical, Engineering and Management Sciences boolean curve fitting boolean equations atomic decomposition cryptography |
| title | Atomic Formulation of the Boolean Curve Fitting Problem |
| title_full | Atomic Formulation of the Boolean Curve Fitting Problem |
| title_fullStr | Atomic Formulation of the Boolean Curve Fitting Problem |
| title_full_unstemmed | Atomic Formulation of the Boolean Curve Fitting Problem |
| title_short | Atomic Formulation of the Boolean Curve Fitting Problem |
| title_sort | atomic formulation of the boolean curve fitting problem |
| topic | boolean curve fitting boolean equations atomic decomposition cryptography |
| url | https://ijmems.in/cms/storage/app/public/uploads/volumes/44-IJMEMS-22-0138-7-5-670-680-2022.pdf |
| work_keys_str_mv | AT ahmedsbalamesh atomicformulationofthebooleancurvefittingproblem AT alimrushdi atomicformulationofthebooleancurvefittingproblem |