Abstract

Boolean derivatives and differentials are used as models for changes in discrete, binary coded systems. Derivatives describe dynamic properties of Boolean functions, e.g. dependence and independence, linearity and monotonicity. They are operators generating other Boolean functions. Equations with derivatives define classes of Boolean functions. Boolean Differentials are models for any kinds of changes, e.g. signal edges, errors, deviations. Equations with differentials define graphs of dynamic systems. A unified theory of derivatives and differentials called Boolean Differential Calculus will be presented.