Exploiting near symmetry in multilevel logic synthesis

Effective algorithms exist for synthesizing symmetric functions and for “ordinary” nonsymmetric functions. However, the existing methods have difficulties when the functions are not symmetric but are “close” to being symmetric. We formulate a set of operations to decompose a function so that symmetric components can be created and utilized to simplify the function. These operations are collectively called symmetry reexpression, and we present theoretical and practical work for performing such operations. The optimal decomposition has exponential complexities; therefore, we seek algorithms to approximate the optimum. The resulting software package applies to arbitrary multilevel Boolean networks. For experimental functions constructed by taking cubes from otherwise symmetric, multiple-output benchmark functions, symmetry reexpression is beneficial when up to 40% of the cubes are removed