McCluskey E. J. Jr. Minimization of Boolean functions. The Bell System technical journal , vol. 35 (1956), pp. 1417–1444.

S. M. AKOVLEV. Teorid struktur kombinatornyh mehanizmov (Theory of the structure of combinatorial mechanisms). Ibid., vol. 19 (1958), pp. 221-227. The author considers the representation by Boolean functions of the structure of certain combinatorial mechanisms so constituted that their similarity to relay circuit structure is almost immediate. Examples of such structures are discussed and include coding and decoding devices in telegraphy, railroad switching control units, and automatic controls in the manufacture of textiles. The fundamental unit of a combinatorial structure consists of several input elements and one output element. Each element may be in one or the other of two positions, normal and transitional, and in either position may be locked or free. For the representation each element is assigned a variable which has the value 0 if the element is in normal position and the value 1 if the element is in transitional position. In addition, each element X which is affected by elements A, B, C, . . . is assigned two functions f(a, b, c, . . . ) and g(a, b, c, . . . ) whose values describe the effect on X of A, B, C, ... as follows. The value of / is 0 if X is locked in normal position and 1 if J? is freed into transitional position for the next operation. The value of g is 0 if X is locked in transitional position and is 1 if X is freed for the next operation in normal position. I t is shown for these structures that one function alone suffices as a Boolean description, since the fundamental units have the properties tha t : (1) f(a, b, c, ...) = 1 if and only if g(a, b, c, . . . ) = 1; (2) for arguments for which / = 0, g is undefined (hence is given the value 0); and (3) for arguments for which g — 0, / is undefined (hence is given the value 0). These fundamental units are connected in series or parallel to form more complex structures, so that a function may be defined for an output element of one of these from simpler functions by means of Boolean operations. The principal application mentioned here for such a representation is in studying the simplification of the structure of a given mechanism through different forms >in terms of Boolean operations of the function which describes the mechanism. Erratum: In order that the two forms of Fx on page 226 hold for the mechanism of Figure 8 on page 225 the lowest horizontal line of that figure should not be locked