bohdan rytsar - Academia.edu (original) (raw)
Papers by bohdan rytsar
Control systems and computers, 2019
The paper presents a new method for the recognition of the different types of total and partial s... more 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.
Abstract. A generalized of conjuncterms simplification rules in polynomial settheoretical format ... more Abstract. A generalized of conjuncterms simplification rules in polynomial settheoretical format has been considered. These rules are based on the proposed theorems for different initial conditions transform of pair conjuncterms, Hamming distance between them can be arbitrary. These rules may be useful to minimize in polynomial set-theoretical format of arbitrary logic functions with n variables. Advantages of the proposed rules of simplification are illustrated by several examples.
2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET), 2018
Decomposition properties of symmetric Boolean functions, represented with the help of the set-the... more Decomposition properties of symmetric Boolean functions, represented with the help of the set-theoretical procedures (q-partition minterms) and constructions (decomposition clones), allowed to simplify logic synthesis of digital combinational circuits. Advantages of the presented set-theoretical approach based on the q-partition minterms are illustrated on the example of logical synthesis of the digital circuit on the basis of the programmable module of FPGA.
Fundamenta Informaticae, 2010
In this paper a creation of new numerical set-theoretical constructions of Boolean functions with... more In this paper a creation of new numerical set-theoretical constructions of Boolean functions with their properties has been presented. The parted conjuncterms and decomposition clones which can be used for realization of different optimization logic synthesis of digital devices and systems have been proposed. Set theoretical operations and procedures with these constructions have been considered. Examples which illustrate simplicity of their practical realization have been presented. Moreover, the paper includes the comparison of new results obtained on the basis of the proposed approach with the results obtained by means of commercial software Quartus II of Altera.
Upravlâûŝie sistemy i mašiny, 2016
UDC 510.63 B.Ye. Rytsar A Simple Numeric Set-Theoretical Method of the Logic Differential Calculu... more UDC 510.63 B.Ye. Rytsar A Simple Numeric Set-Theoretical Method of the Logic Differential Calculus Предложен новый метод логического дифференциального исчисления на основании числового теоретико-множественного подхода к определению разных типов логических производных произвольного порядка от булевой функции. Алгоритм имеет относительно меньшую вычислительную сложность при меньшем количестве операций, необходимых для решения задачи, что подтверждено примерами определения разных логических производных произвольных порядков от функций, заимствованных авторами из известных публикаций в порядке сравнения с предложенным методом. A new method of the logic differential calculus, based on the numeric set-theoretical approach for the definition of the different logic derivatives types of the arbitrary order for Boolean function is proposed. The given algorithm has relatively less computational complexity due to the lower amount of the operations required for solving the given problem. This is proved in the given examples borrowed from the well-known publications, in order to compare them with the proposed numeric set-theoretic method to obtain the different types of logic derivatives of arbitrary order. Запропоновано новий метод логічного диференційного числення на основі числового теоретико-множинного підходу до визначення різних типів логічних похідних довільного порядку від бульової функції. Алгоритм має відносно меншу обчислювальну складність за меншої кількості операцій, необхідних для розв'язання задачі, що підтверджено прикладами визначення запропонованим методом різних логічних похідних довільних порядків від функцій, запозичених авторами з відомих публікацій з метою порівняння з пропонованим методом. Introduction. The modern methods of the logic design of digital devices and systems more often include the elements of the logic differential calculus [1-21]. This is related to qualitatively new possibilities of informational technologies and, consequently, to solving new problems of design and analysis of dynamic systems. In the survey [5, 7] the main directions, modern achievements and tendencies of the research in various branches of science and engineering is represented and fully analysed. Among them there are recearch on sensitivity of the combination network to changes of separate variables or their groups of the logic function that describes [9], testing the logic schema aimed at determining its faultiness at its arbitrary point [10-12], functional decomposition [1, 11, 13], minimization in the class of Reed-Muller's forms of different polarity [14], identification of symmetry [15, 16], and different optimization of problems of logic synthesis of digital devices and systems [12, 17, 18], etc. The main obstacle to wide application of the logic derivatives in different aspects of research is the complexity of the practical realization of their determination (calculation) in case of high orders and large number of variables [9]. Traditional symbolic transformations or visual methods based on Karnaugh maps [2-4] and patterns of Boolean functions [20] do not satisfy the requirements of the modern practice. Determination of the logic derivatives from the axioms and theorems of Boolean algebra and simplification of obtained analytical expressions is quite difficult and tedious. The application of matrix device based in particular on FFT-like algorithms enabled us to automate the process of the logic differential calculus [3, 5, 8, 21]. However, as mentioned in [5, 7], the realization of the matrix transformations in the case of many variables is difficult, and in addition, cumbersome, since the calculation of Kronecker product, which is used for this, even in case of a simple derivative with respect to one variable for a function of n variables the dimension of the matrix must be 2 2 n n . These shortcomings become particularly noticeable when calculating the logic derivatives of high orders. We represent a new method of the logic differential calculus based on the numeric set-theoretical approach for definition of different logic derivatives types of the arbitrary order for Boolean function. The proposed method is compared with the known analytical, visual and matrix methods, relatively simpler as to its practical realization manually as well as with the assistance of computer without any previous transformations of Boolean function given in set-theoretical format. The presented algorithm has relatively less computational complexity due to lower amount of the operations required.
2008 International Conference on Modern Problems of Radio Engineering Telecommunications and Computer Science, Feb 1, 2008
BRASh functional decomposition program has been described. The algorithm of the program is based ... more BRASh functional decomposition program has been described. The algorithm of the program is based on q-partition method. BRASh program efficiency for the problem of logical synthesis of combinational networks has been shown on the example of synthesis of benchmark functions.
Proceedings of the International Conference Modern Problems of Radio Engineering Telecommunications and Computer Science 2004, Mar 24, 2004
The set-theoretical modification of minimax covering method of Boolean functions has been conside... more The set-theoretical modification of minimax covering method of Boolean functions has been considered. The modificated method is based on the proposed procedure of prime conjuncterms weighing. As distinct from traditional ones, the proposed algorithm allows correction of the covering progress by choosing a shorter way.
The Experience of Designing and Application of CAD Systems in Microelectronics, 2003. CADSM 2003. Proceedings of the 7th International Conference.
The new encoding method of subfunctions in the task of PLA synthesis of digital devices by the th... more The new encoding method of subfunctions in the task of PLA synthesis of digital devices by the theoretical-set of functional decomposition has been offered. The method is based on so-called initial encoding and preserves a block structure of the minimized SOP-form of functions system. The advantage of method is illustrated by the example of PLA-realisation of bi-decomposition.
5th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Service. TELSIKS 2001. Proceedings of Papers (Cat. No.01EX517), 2001
A new approach to the decomposition of Boolean functions of n variables has been considered. This... more A new approach to the decomposition of Boolean functions of n variables has been considered. This approach is based on the minterm q-partition method and the introduced concept of decomposition clones. A theorem about disjunctive decomposition of systems of complete and partial functions has been formulated. The suggested method is illustrated by an example.
2008 Conference on Human System Interactions, 2008
A new approach to the functional decomposition based on the theoretical-set method of q-partition... more A new approach to the functional decomposition based on the theoretical-set method of q-partition numerical conjuncterms and an introduced concept of decomposition clones of different given forms of Boolean functions of n variables has been considered. The theorem about disjoint compatible decomposition of functions system has been formulated. The suggested algorithm is illustrated by examples.
2007 9th International Conference - The Experience of Designing and Applications of CAD Systems in Microelectronics, 2007
The algorithm and program BRASh for partitive block-recured decomposition of Boolean function has... more The algorithm and program BRASh for partitive block-recured decomposition of Boolean function has been given. It is based on the q-minterm partitioning. The proposed algorithm has a simpler computer realization due to using of structured sets in other words decomposition clones.
2006 International Conference - Modern Problems of Radio Engineering, Telecommunications, and Computer Science, 2006
The manufacturing cost of a component is direction proportional to the difference between the low... more The manufacturing cost of a component is direction proportional to the difference between the lower and upper specification limits and the functional aspects of the assembly of two components are also affected by the magnitude of fit between those components. In the present work detail, a study of interference fit between coupling and shaft in a steam turbine is carried out. Under normal operating conditions, the coupling hub is expected to transmit 75 MW at the rated speed of 3000 RPM. The interference fit between the motor and turbine to transmit the torque is analyzed by estimating the contact pressure between the coupling and shaft using 2D FEM analysis. The analysis were performed for: (i) Standstill condition, (ii) Operating at the rated speed with short circuit conditions, equivalent to 4.4 times the nominal power transmission and (iii) Operating at rated torque but higher (121% of the rated) speed conditions. The analysis for each cases is performed by having two different type of meshing (i) uniform meshing and (ii) fine meshing at the contact zone and (i) contact pressure, (ii) Tangential stress distribution and (iii)Von-mises stress is estimated. The validation of FEM method was performed by comparing the theoretical and estimated reduction in contact pressure. The maximum value of power developed for the present case is estimated.
Current Ukrainian Research in Optics and Photonics: Optoelectronic and Hybrid Optical/Digital Systems for Image Processing, 1997
Cybernetics and Systems Analysis, 2007
The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean... more The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean functions of variables specified in different representation forms. The approach is based on the method of q-partitions of conjuncterms and concept of decomposition clones. Theorems on joint decomposition of a system of full and partial functions are formulated. The approach is illustrated by examples.
Cybernetics and Systems Analysis, 2007
The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean... more The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean functions of variables specified in different representation forms. The approach is based on the method of q-partitions of conjuncterms and concept of decomposition clones. Theorems on joint decomposition of a system of full and partial functions are formulated. The approach is illustrated by examples.
Control systems and computers, 2019
The paper presents a new method for the recognition of the different types of total and partial s... more 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.
Abstract. A generalized of conjuncterms simplification rules in polynomial settheoretical format ... more Abstract. A generalized of conjuncterms simplification rules in polynomial settheoretical format has been considered. These rules are based on the proposed theorems for different initial conditions transform of pair conjuncterms, Hamming distance between them can be arbitrary. These rules may be useful to minimize in polynomial set-theoretical format of arbitrary logic functions with n variables. Advantages of the proposed rules of simplification are illustrated by several examples.
2018 14th International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering (TCSET), 2018
Decomposition properties of symmetric Boolean functions, represented with the help of the set-the... more Decomposition properties of symmetric Boolean functions, represented with the help of the set-theoretical procedures (q-partition minterms) and constructions (decomposition clones), allowed to simplify logic synthesis of digital combinational circuits. Advantages of the presented set-theoretical approach based on the q-partition minterms are illustrated on the example of logical synthesis of the digital circuit on the basis of the programmable module of FPGA.
Fundamenta Informaticae, 2010
In this paper a creation of new numerical set-theoretical constructions of Boolean functions with... more In this paper a creation of new numerical set-theoretical constructions of Boolean functions with their properties has been presented. The parted conjuncterms and decomposition clones which can be used for realization of different optimization logic synthesis of digital devices and systems have been proposed. Set theoretical operations and procedures with these constructions have been considered. Examples which illustrate simplicity of their practical realization have been presented. Moreover, the paper includes the comparison of new results obtained on the basis of the proposed approach with the results obtained by means of commercial software Quartus II of Altera.
Upravlâûŝie sistemy i mašiny, 2016
UDC 510.63 B.Ye. Rytsar A Simple Numeric Set-Theoretical Method of the Logic Differential Calculu... more UDC 510.63 B.Ye. Rytsar A Simple Numeric Set-Theoretical Method of the Logic Differential Calculus Предложен новый метод логического дифференциального исчисления на основании числового теоретико-множественного подхода к определению разных типов логических производных произвольного порядка от булевой функции. Алгоритм имеет относительно меньшую вычислительную сложность при меньшем количестве операций, необходимых для решения задачи, что подтверждено примерами определения разных логических производных произвольных порядков от функций, заимствованных авторами из известных публикаций в порядке сравнения с предложенным методом. A new method of the logic differential calculus, based on the numeric set-theoretical approach for the definition of the different logic derivatives types of the arbitrary order for Boolean function is proposed. The given algorithm has relatively less computational complexity due to the lower amount of the operations required for solving the given problem. This is proved in the given examples borrowed from the well-known publications, in order to compare them with the proposed numeric set-theoretic method to obtain the different types of logic derivatives of arbitrary order. Запропоновано новий метод логічного диференційного числення на основі числового теоретико-множинного підходу до визначення різних типів логічних похідних довільного порядку від бульової функції. Алгоритм має відносно меншу обчислювальну складність за меншої кількості операцій, необхідних для розв'язання задачі, що підтверджено прикладами визначення запропонованим методом різних логічних похідних довільних порядків від функцій, запозичених авторами з відомих публікацій з метою порівняння з пропонованим методом. Introduction. The modern methods of the logic design of digital devices and systems more often include the elements of the logic differential calculus [1-21]. This is related to qualitatively new possibilities of informational technologies and, consequently, to solving new problems of design and analysis of dynamic systems. In the survey [5, 7] the main directions, modern achievements and tendencies of the research in various branches of science and engineering is represented and fully analysed. Among them there are recearch on sensitivity of the combination network to changes of separate variables or their groups of the logic function that describes [9], testing the logic schema aimed at determining its faultiness at its arbitrary point [10-12], functional decomposition [1, 11, 13], minimization in the class of Reed-Muller's forms of different polarity [14], identification of symmetry [15, 16], and different optimization of problems of logic synthesis of digital devices and systems [12, 17, 18], etc. The main obstacle to wide application of the logic derivatives in different aspects of research is the complexity of the practical realization of their determination (calculation) in case of high orders and large number of variables [9]. Traditional symbolic transformations or visual methods based on Karnaugh maps [2-4] and patterns of Boolean functions [20] do not satisfy the requirements of the modern practice. Determination of the logic derivatives from the axioms and theorems of Boolean algebra and simplification of obtained analytical expressions is quite difficult and tedious. The application of matrix device based in particular on FFT-like algorithms enabled us to automate the process of the logic differential calculus [3, 5, 8, 21]. However, as mentioned in [5, 7], the realization of the matrix transformations in the case of many variables is difficult, and in addition, cumbersome, since the calculation of Kronecker product, which is used for this, even in case of a simple derivative with respect to one variable for a function of n variables the dimension of the matrix must be 2 2 n n . These shortcomings become particularly noticeable when calculating the logic derivatives of high orders. We represent a new method of the logic differential calculus based on the numeric set-theoretical approach for definition of different logic derivatives types of the arbitrary order for Boolean function. The proposed method is compared with the known analytical, visual and matrix methods, relatively simpler as to its practical realization manually as well as with the assistance of computer without any previous transformations of Boolean function given in set-theoretical format. The presented algorithm has relatively less computational complexity due to lower amount of the operations required.
2008 International Conference on Modern Problems of Radio Engineering Telecommunications and Computer Science, Feb 1, 2008
BRASh functional decomposition program has been described. The algorithm of the program is based ... more BRASh functional decomposition program has been described. The algorithm of the program is based on q-partition method. BRASh program efficiency for the problem of logical synthesis of combinational networks has been shown on the example of synthesis of benchmark functions.
Proceedings of the International Conference Modern Problems of Radio Engineering Telecommunications and Computer Science 2004, Mar 24, 2004
The set-theoretical modification of minimax covering method of Boolean functions has been conside... more The set-theoretical modification of minimax covering method of Boolean functions has been considered. The modificated method is based on the proposed procedure of prime conjuncterms weighing. As distinct from traditional ones, the proposed algorithm allows correction of the covering progress by choosing a shorter way.
The Experience of Designing and Application of CAD Systems in Microelectronics, 2003. CADSM 2003. Proceedings of the 7th International Conference.
The new encoding method of subfunctions in the task of PLA synthesis of digital devices by the th... more The new encoding method of subfunctions in the task of PLA synthesis of digital devices by the theoretical-set of functional decomposition has been offered. The method is based on so-called initial encoding and preserves a block structure of the minimized SOP-form of functions system. The advantage of method is illustrated by the example of PLA-realisation of bi-decomposition.
5th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Service. TELSIKS 2001. Proceedings of Papers (Cat. No.01EX517), 2001
A new approach to the decomposition of Boolean functions of n variables has been considered. This... more A new approach to the decomposition of Boolean functions of n variables has been considered. This approach is based on the minterm q-partition method and the introduced concept of decomposition clones. A theorem about disjunctive decomposition of systems of complete and partial functions has been formulated. The suggested method is illustrated by an example.
2008 Conference on Human System Interactions, 2008
A new approach to the functional decomposition based on the theoretical-set method of q-partition... more A new approach to the functional decomposition based on the theoretical-set method of q-partition numerical conjuncterms and an introduced concept of decomposition clones of different given forms of Boolean functions of n variables has been considered. The theorem about disjoint compatible decomposition of functions system has been formulated. The suggested algorithm is illustrated by examples.
2007 9th International Conference - The Experience of Designing and Applications of CAD Systems in Microelectronics, 2007
The algorithm and program BRASh for partitive block-recured decomposition of Boolean function has... more The algorithm and program BRASh for partitive block-recured decomposition of Boolean function has been given. It is based on the q-minterm partitioning. The proposed algorithm has a simpler computer realization due to using of structured sets in other words decomposition clones.
2006 International Conference - Modern Problems of Radio Engineering, Telecommunications, and Computer Science, 2006
The manufacturing cost of a component is direction proportional to the difference between the low... more The manufacturing cost of a component is direction proportional to the difference between the lower and upper specification limits and the functional aspects of the assembly of two components are also affected by the magnitude of fit between those components. In the present work detail, a study of interference fit between coupling and shaft in a steam turbine is carried out. Under normal operating conditions, the coupling hub is expected to transmit 75 MW at the rated speed of 3000 RPM. The interference fit between the motor and turbine to transmit the torque is analyzed by estimating the contact pressure between the coupling and shaft using 2D FEM analysis. The analysis were performed for: (i) Standstill condition, (ii) Operating at the rated speed with short circuit conditions, equivalent to 4.4 times the nominal power transmission and (iii) Operating at rated torque but higher (121% of the rated) speed conditions. The analysis for each cases is performed by having two different type of meshing (i) uniform meshing and (ii) fine meshing at the contact zone and (i) contact pressure, (ii) Tangential stress distribution and (iii)Von-mises stress is estimated. The validation of FEM method was performed by comparing the theoretical and estimated reduction in contact pressure. The maximum value of power developed for the present case is estimated.
Current Ukrainian Research in Optics and Photonics: Optoelectronic and Hybrid Optical/Digital Systems for Image Processing, 1997
Cybernetics and Systems Analysis, 2007
The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean... more The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean functions of variables specified in different representation forms. The approach is based on the method of q-partitions of conjuncterms and concept of decomposition clones. Theorems on joint decomposition of a system of full and partial functions are formulated. The approach is illustrated by examples.
Cybernetics and Systems Analysis, 2007
The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean... more The paper considers the set-theoretical approach to the joint decomposition of systems of Boolean functions of variables specified in different representation forms. The approach is based on the method of q-partitions of conjuncterms and concept of decomposition clones. Theorems on joint decomposition of a system of full and partial functions are formulated. The approach is illustrated by examples.