Reed-Muller function optimization techniques with onset table

By mapping a fixed polarity Reed-Muller （RM） expression into an onset table and studying the properties of the onset table, an algorithm is proposed to obtain a compact multi-level single-output mixed-polarity RM function by searching for and extracting the common variables using the onset table. Furthermore, by employing the multiplexer model, the algorithm is extended to optimize multi-level multi-output mixed-polarity RM forms. The proposed algorithm is implemented in C language and tested using some MCNC benchmarks. Experimental results show that the proposed algorithm can obtain a more compact RM form than that under fixed polarity. Compared with published results, the proposed algorithm makes a significant speed improvement, with a small increase in the number of literals.