A new approach to the decomposition of incompletely specified multi-output functions based on graph coloring and local transformations and its application to FPGA mapping

Abstract

An approach to the decomposition of incompletely specified Boolean functions is introduced, and its application to lookup-table-based field programmable gate array (FPGA) mapping is described. Three methods are developed: fast graph coloring to perform a quasi-optimum 'don't care' assignment; variable partitioning to quickly find the 'best' partitions; and local transformation to transform a nondecomposable function into several decomposable ones. The methods perform global optimization of the input function. A short description of a FPGA mapping program (TRADE) and an evaluation of its results are provided.<>