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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 401616, 13 pages
http://dx.doi.org/10.1155/2013/401616
Research Article

A Generalized If-Then-Else Operator for the Representation of Multi-Output Functions

1School of Education, Tel-Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
2School of Engineering, Bar-Ilan University, Ramat-Gan 52900, Israel

Received 6 September 2012; Revised 30 December 2012; Accepted 22 January 2013

Academic Editor: Bozidar Sarler

Copyright © 2013 Ilya Levin and Osnat Keren. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper deals with fundamentals of systems of Boolean functions called multi-output functions (MOFs). A new approach to representing MOFs is introduced based on a Generalized If-Then-Else (GITE) function. It is shown that known operations on MOFs may be expressed by a GITE function. The GITE forms the algebra of MOFs. We use the properties of this algebra to solve an MOF-decomposition problem. The solution provides a compact representation of MOFs.