Encoding multi-valued functions for symmetry

In high-level designs, variables are often naturally represented in a symbolic multi-valued form. Binary encoding is an essential step in realizing these designs in Boolean circuits. This paper poses the encoding problem with the objective of maximizing the degree of symmetry, which has many useful applications in logic optimization, circuit rewiring, functional decomposition, etc. In fact, it is guaranteed that there exists a full symmetry encoding with respect to every input multivalued variable for all multi-valued functions. We propose effective computation for finding such encoding by solving a system of subset-sum constraints. Experiments show unique benefits of symmetry encoding.