GENERALIZATION OF THE SHANNON EXPANSION FOR INCOMPLETELY SPECIFIED FUNCTIONS: THEORY AND APPLICATION - A. A. Prikhozhy (Системный анализ и прикладная информатика)
The well known Shannon expansion is not applicable to incompletely specified functions. We propose a theory that merges Boolean and partial algebras and provides creation of new representations and expansions of partially specified functions. A powerful property of the expansions is the reduction of definiteness level of expansion products. This is a source of enlargement of possibilities for synthesis, parallelization and optimization of completely and incompletely specified logical software/hardware systems. A result of proposed theory is a new type of decision diagram. It is shown on the parallelization of adders that the throughput of the system grows rapidly while the system complexity grows slowly.