Minimization of incompletely specified mixed polarity Reed Muller functions using genetic algorithm.

Al-Jassani, ban Adil; Urquhart, Neil B; Almaini, A E A

Abstract

A New and efficient Genetic Algorithm (GA) based approach is presented to minimise the number of terms of Mixed Polarity Reed Muller (MPRM) single and multi output incompletely specified Boolean functions. The algorithm determines the allocation of don’t care terms for the given function resulting in optimal MPRM expansions. For an n-variable function with ? unspecified minterms there are (3n × 2?) distinct MPRM expansions. A minimum MPRM is one with the fewest products. The algorithm is implemented in C++ and fully tested using standard benchmark examples. For the benchmark examples tested, the number of terms is reduced, on average, by 49% if “don’t care” terms are included.

• Conference Name: 3rd IEEE international conference on Signal Circuits and Systems
• Start Date: Nov 6, 2009
• End Date: Nov 8, 2009
• Publication Date: 2009-11
• Deposit Date: Jan 15, 2010
• Publicly Available Date: Jan 15, 2010
• Peer Reviewed: Peer Reviewed
• ISBN: 978-1-4244-4398-7
• DOI: https://doi.org/10.1109/12.67320
• Keywords: Mixed Polarity Reed Muller; incompletely specified Boolean functions; aenetic algorithm
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/3500
• Contract Date: Jan 15, 2010