Bit-level and word-level polynomial expressions for functions in Fibonacci interconnection topologies

Abstract

In this paper, we extend various Boolean representations for switching functions, as SOPs, Reed-Muller expressions, Kronecker, and Pseudo Kronecker ANDEXOR expressions, to functions used in Fibonacci interconnection topologies. Then, we extend the world-level expressions, as arithmetic expressions, and Walsh expressions, to these functions. We introduce the corresponding decision diagrams as graphic representations of these bit-level and word-level expressions, In this way, we proVide a base to extend the application of powerful CAD design tools using polynomial expressions and DDs for switching functions to functions in Fibonacci interconnection topologies.