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Functions Implicitly Defined by Logic Equations-Unique Solutions

The problem of resolving restrictive logic equations occurs in the analysis and synthesis of digital systems. The implicit representation of logic functions is useful to describe the behavior of the systems, and the explicit unique representation is needed to describe the structure. The main aim of this paper is to show an easy way to find candidates of functions, resolving the given equation in a unique way, and to check that these functions are valid. In order to do this, the basic definitions of derivative operations are introduced, and, by using an inductive approach, suitable algorithms are suggested and evaluated. Quantitative results about the uniquely resolvable equations show finally some surprising results.