Boolean Differential Equations
نویسندگان
چکیده
The expressiveness of Boolean Algebras is significantly extended by the Boolean Differential Calculus (BDC). The additionally defined differentials of Boolean variables, differentials and further differential operators of Boolean functions as well as several derivative operations of Boolean functions allow to model changes of function values together with changes of the values of variables and many other properties of Boolean functions. A Boolean equation equals two given Boolean functions. Its solution is a set of Boolean vectors. We introduce in this paper Boolean Differential Equations (BDE). A BDE is an equation that includes derivative operations and differential operators of an unknown Boolean function. We show in this paper that, completely different from a Boolean equation, the solution of a Boolean differential equation is a set of Boolean functions. Hence, Boolean differential equations allow to describe and handle sets of Boolean functions. For an easier understanding we repeat the definition of the derivative operations and explain the essentials of Boolean differential equations using an example of the most restricted BDE. For a special class of Boolean differential equations we introduce the theoretical background for its solution and give a very simple solution algorithm. Furthermore we show how more general classes can be solved.
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