Minimization of Quaternary Galois Field Sum of Products Expression for Multi-Output Quaternary Logic Function Using Quaternary Galois Field Decision Diagram

• Published in: 38th International Symposium on Multiple Valued Logic (ismvl 2008) pp. 125 - 130
• Main Authors: Khan, M.H.A., Siddika, N.K., Perkowski, M.A.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-05-2008
• Subjects: Arithmetic; Computer science; Galois fields; Heuristic algorithms; Java; Logic functions; Minimization; Multivalued logic; Wire
• ISBN: 9780769531557; 0769531555
• ISSN: 0195-623X; 2378-2226
• DOI: 10.1109/ISMVL.2008.31

A quaternary logic function expressed as quaternary Galois field sum of products (QGFSOP) expression can be realized as a cascade of quaternary 1-qudit, Feynman, and Toffoli gates. In this paper, we have presented a heuristic algorithm for simultaneous variable ordering and quaternary Galois field expansion selection for constructing optimal quaternary Galois field decision diagram (QGFDD). We have also shown the way of flattening the QGFDD for generating QGFSOP expression. We have written Java program to construct QGFDD for multi-output quaternary functions and provided experimental results.