Decomposition of Boolean Functions Speciied by Cubes

We study the problem of decomposing a Boolean function into a set of functions with fewer arguments. This problem has considerable practical importance in VLSI. For example, for digital circuits designed with eld-programmable gate arrays, it is necessary to express Boolean functions in terms of`smaller' functions that t the cells of the array. The decomposition problem is old, and well understood when the function to be decomposed is speciied by a truth table listing the function's minterms, or has one output only. However, modern design tools, such as Berkeley's Espresso, handle functions with many outputs and represent them by Boolean cubes rather than minterms, for reasons of eeciency. In this paper we develop a decomposition theory for multiple-output, partially speciied Boolean functions represented by cubes. The theory uses ternary algebra and generalized set systems.