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

Article type: Research Article

Authors: Rytsar, Bohdan | Romanowski, Piotr | Shvay, Adrian

Affiliations: Rzeszow University, Chair of Computer Science, Dekerta str. 2 35-030 Rzeszow, Poland. E-mail: bohdan@rytsar.com; proman@univ.rzeszow.pl | National University "Lviv Polytechnic", S. Bandery Str., 12, L'viv, 79646, Ukraine

Abstract: 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.

Keywords: Boolean function, set-theoretical constructions, decomposition, parted conjuncterm, decomposition clone

DOI: 10.3233/FI-2010-253

Journal: Fundamenta Informaticae, vol. 99, no. 3, pp. 339-354, 2010