Abstract
It is well known that Exclusive Sum-Of-Products (ESOP) expressions for Boolean functions require on average the smallest number of cubes. Thus, a simple complexity measure for a Boolean function is the number of cubes in its simplest ESOP. It will be shown that this structure-oriented measure of the complexity can be improved by a unique complexity measure which is based on the function. Thus, it is suggested to detect all most complex Boolean functions more precisely by means of the Specialized Normal Form (SNF). The SNF is a unique (canonical) ESOP representation of a Boolean function. In this paper properties of the most complex Boolean functions are studied. Adjacency graphs of the SNF will be used to calculate minimal ESOPs as well as to detect special properties of most complex Boolean functions. These properties affect the procedure of finding exact minimal ESOPs. A solution is given that overcomes these observed problems. Using the SNF, the number of most complex Boolean functions was found. A recursive algorithm will be given that calculates each most complex Boolean function for a given number of variables.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Facta universitatis - series: Electronics and Energetics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
