Communication based FPGA synthesis for multi-output Boolean functions

Abstract

One of the crucial problems multi level logic synthesis techniques for multi output Boolean functions f=(f/sub 1/,...,f/sub m/):{0,1}/sup n//spl rarr/{0,1}/sup m/ have to deal with is finding sublogic which can be shared by different outputs, i.e., finding Boolean functions /spl alpha/=(/spl alpha//sub 1/,...,/spl alpha//sub h/):{0,1}/sup p//spl rarr/{0,1}/sup h/ which can be used as common sublogic of good realizations of f/sub 1/,...,f/sub m/. We present an efficient ROBDD based implementation of this common decomposition functions problem (CDF). Formally, CDF is defined as follows: given m Boolean functions f/sub 1/,...,f/sub m/:{0,1}/sup n//spl rarr/{0,1}, and two natural numbers p and h, find h Boolean functions /spl alpha//sub 1/,..., /spl alpha//sub h/:{0, 1}/sup p//spl rarr/{0,1} such that /spl forall/1/spl les/k/spl les/m there is a decomposition of f/sub k/ of the form: f/sub k/(x/sub 1/,...x/sub n/)=g/sup (k)/(/spl alpha//sub 1/(x/sub 1/,...x/sub p/),...,/spl alpha//sub h/(x/sub 1/,...,x/sub p/),/spl alpha//sub h+1//sup (k)/(x/sub 1/,...,x/sub p/),...,/spl alpha/(r/sub k/)/sup (k)/(x/sub 1/,...x/sub p/),x/sub p+1/,...,x/sub n/) using a minimal number r/sub k/ of single output Boolean decomposition functions. Experimental results applying the method to FPGA synthesis are promising.