Computing support-minimal subfunctions during functional decomposition

The growing popularity of look-up table (LUT)-based field programmable gate arrays (FPGA's) has renewed the interest in functional or Roth-Karp decomposition techniques. Functional decomposition is a powerful decomposition method that breaks a Boolean function into a set of subfunctions and a composition function. Little attention has so far been given to the problem of selecting good subfunctions after partitioning the input variables into the disjoint bound and free sets. Therefore, the extracted subfunctions usually depend on all bound variables. In this paper, we present a novel decomposition algorithm that computes subfunctions with a minimal number of inputs. This reduces the number of LUT's and improves the usage of multiple-output SRAM cells. The algorithm iteratively computes subfunctions; in each iteration step it implicitly computes a set of possible subfunctions and finds a subfunction with minimal support. Moreover, our technique finds nondisjoint decompositions, and thus unifies disjoint and nondisjoint decomposition. The algorithm is very fast and yields substantial reductions of the number of LUT's and SRAM cells.