Functional Multiple-Output Decomposition: Theory and an Implicit Algorithm

We present theory and a novel, implicit algorithm for functional disjoint decomposition of multiple-output functions. While a Boolean function usually has a huge number of decomposition functions, we show that not all of them are useful for multiple-output decomposition. We therefore introduce the concept of preferable decomposition functions, which are sufficient for optimal multiple-output decomposition. We describe how to implicitly compute all preferable decomposition functions of a single-output, and how to identify all common preferable decomposition functions of a multiple-output function. Due to the implicit computation in all steps, the algorithm is very efficient. Applied to FPGA synthesis, the method combines the typically separated steps of common subfunction extraction and technology mapping. Experimental results show significant reductions in area.