Cube‐Based Synthesis of ESOPs for Large Functions

This study focuses on low‐complexity synthesis of Exclusive‐or sum‐of‐products expansions (ESOPs). A scalable cube‐based method, which only uses iterative executions of cube intersection and subcover minimization for cube set expressions, is presented to obtain quasi‐optimal ESOPs for completely specified multi‐output functions. For deriving canonical Reed‐Muller (RM) forms, four conversion rules of cubes are proposed to achieve fast conversion between a canonical form and an Exclusiveor sum‐of‐products (ESOP) or between different canonical forms. Numerical examples are given to verify the correctness of cube‐based minimization and conversion methods. The proposed methods have been implemented in C language and tested on a large set of MCNC benchmark functions (ranging from 5 to 201 inputs). Experimental results show that, compared with existing methods, ours can reduce the number of cubes by 27% and save the CPU time by 74% on average in the final solution of minimization, and consume less time as well during the conversion process. As a whole, our methods are efficient in terms of both memory space and CPU time and can be able to deal with very large functions.