The paper deals with the schemes of functional elements of a special kind that implement Boolean functions. The schemes in question are mathematical models of integral schemes, which are the main part of all computational electronic structures. The size, area, volume, location of nodes and communication channels are taken into account in assessing the complexity of Boolean functions implementation. We obtain the exact lower estimates of the complexity of the implementation of some Boolean functions and systems of Boolean functions, as well as the ratio of the complexities of plane and volume schemes.

implementation of Boolean functions, lower estimates of the complexity, the synthesis of schemes consisting of functional elements, mathematical model of integral schemes.

Mathematical problems and theory of numerical methods