Set-theoretical Constructions of Boolean Functions and theirs Applications in Logic Synthesis

• Autorzy: Rytsar B. , Romanowski P. , Shvay A.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Boolean function; set-theoretical constructions; decomposition; parted conjuncterm; decomposition clone

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2010
• Tom: Vol. 99, nr 3
• Strony: 339--354
• Opis fizyczny: Bibliogr. 11 poz., tab.

Twórcy

autor

Rytsar B.

autor

Romanowski P.

autor

Shvay A.

• Rzeszow University, Chair of Computer Science, Dekerta str. 2 35-030 Rzeszow, Poland,

Bibliografia

• [1] McCluskey E.: Logic Design Principles, Prentice-Hall, Englewood Cliffs, NJ, 1986.
• [2] Giovanni De Michelli, Synthesis and Optimization of Digital Circuits, Stanford University, 1994, McGraw-Hill, Inc., 631 p.
• [3] Representations of Discrete Functions (ed. by T. Sasao and M. Fujita), Kluwer Academic Publishers, Boston/London/Dordrecht, 1996.
• [4] Zakrevskij A., Toropov N.: Polynomial Implementation of Incompletely Specified Boolean Functions and Systems, Minsk: Institute of Engineering Cybernetics of National Academy of Sciences of Belarus, 2001. - 200 p. (in Russian).
• [5] Rytsar B. Y.: A New Approach to the Decomposition of Boolean Functions by the Method of q- Partitions. I. Separating Decomposition of Full and Partial Functions, Cybernetics and Systems Analysis, September 2001, vol. 37, no. 5, pp. 654-676.
• [6] Rytsar B. Y.: A New Approach to the Decomposition of Boolean Functions by the Method of q-Partitions. II. Repeated Decomposition, Cybernetics and Systems Analysis, January 2002, vol. 38, no. 1, pp. 44-52.
• [7] Rytsar B. Y.: A New Approach to the Decomposition of Boolean Functions by the Method of q-Partitions. III. Joint decomposition of a function system, Cybernetics and Systems Analysis, March 2007, vol. 43, no. 2, pp. 192-207(16).
• [8] Rytsar B. Y., Shvay. A.: Algorithm and Program for Block-Recurred Functional Decomposition Using q Partition Method, Proc. 9th Inter. Conf. "The experience of designing and application of CAD system in microelectronics", Polyana, Ukraine, 19-24 Feb., 2007.
• [9] Rytsar B. Y.: A Method of Symmetry Detection and Recognition in Boolean Function, Control Systems and Computers, 2001, no. 4, pp. 13-41. (in Ukrainian and Russian)
• [10] Rytsar B. Y.: The logic synthesis of combinational networks on the base multiplexers by q-partition conjuncterms method, Control Systems and Computers, 2006, no. 3, pp. 51-61. (in Ukrainian and Russian)
• [11] Rytsar B. Y., Kmet' A. B.: A NewMethod of CodingMinorants in Problems of Synthesis of Digital Devices from PLAs, Cybernetics and Systems Analysis, vol. 39, Issue 2, March - April 2003, pp. 212-234.