Multilevel logic simplification based on a containment recursive paradigm

Multilevel logic simplification plays a very important role to achieve high quality digital circuits in the design flow of application specific integrated circuit or a field programmable gate array products. The fundamental concept of unateness, is extended to the concept of containment for Boolean functions. Accordingly, the unate recursive paradigm, which is successfully employed in the two-level logic minimisation, is adapted to containment recursive paradigm for multilevel logic simplification of incompletely specified multiple output Boolean functions. Consequently, the functional ‘don't cares’ of Boolean functions can be extracted and utilised based on the functionality, instead of the structural information like satisfiability don't cares and observability don't cares. The efficient application of functional don't cares is developed with respect to variable order and splitting equation strategies based on containment recursive paradigm. Furthermore, the algorithm is generalised to multiple output functions using an encoding method. Experimental results show that the containment recursive paradigm is fundamental and effective for multilevel logic simplification.