Encoding of Boolean Functions and its Application to LUT Cascade Synthesis

The problem of encoding arises in several areas of logic synthesis. Due to the nature of this problem, it is often difficult to systematically explore the space of all feasible encodings in order to find an optimal one. In this paper, we show that when the objects to be encoded are Boolean functions, it is possible to formulate and solve the problem optimally. We present a general approach to the encoding problem with one or more code-bit functions having some desirable properties. The method allows for an efficient implementation using branch-and-bound procedure coupled with specialized BDD operators. The proposed approach was used to synthesize look-up table (LUT) cascades implementing Boolean functions. Experimental results show that it finds optimal solutions for complex encoding problems in less than a second of CPU time.