Multi-level optimisation of fixed polarity Reed-Muller expansions using Reed-Muller binary decision diagrams

The Reed-Muller binary decision diagram (RMBDD) is an alternative way of representing generalised Reed-Muller (GRM) expansions. This graphical representation provides a complete canonical description of GRM functions and is a counterpart of the well-known Boolean binary decision diagram. The structure of RMBDDs and rules for reducing the size of the diagrams are described in this paper; additionally, ordered RMBDDs are introduced. An algorithm which determines a good variable order without performing an exhaustive search is described. The physical implementations of the RMBDDs using RM-ULMs and at gate level are also discussed in this paper