Аннотация:In general, a cellular circuit of functional and switching elements is a mathematicalmodel of integrated circuits and, first of all, very large-scale integrated circuits (VLSIs), whichtake into account the features of their physical synthesis. The fundamental difference of this modelfrom the well-studied classes of circuits of functional elements (Boolean circuits) is the presenceof additional requirements for the geometry of the circuit, which ensure that the necessary routingresources are taken into account when creating VLSI. The subject of study by many authors wasthe complexity of the implementation of the so-called universal multipole of order n, n = 1, 2,...,that is, systems of all functions of the algebra of logic in n Boolean variables in various classes ofcircuits. In this paper, we establish asymptotically tight bounds of a high degree of accuracy for thearea of cellular circuits. At the same time, a family of circuit universal multipoles of order n with anarea equal to the upper bound is constructively built, and a method for obtaining the correspondinglower bound is proposed.
