Full Subtracter Circuit. Part II

The articles [17], [16], [21], [15], [3], [18], [25], [1], [9], [10], [4], [8], [2], [19], [24], [14], [20], [13], [12], [11], [23], [5], [7], and [22] provide the terminology and notation for this paper. Let n be a natural number and let x, y be finite sequences. The functor n-BitSubtracterStr(x, y) yields an unsplit non void strict non empty many sorted signature with arity held in gates and Boolean denotation held in gates and is defined by the condition (Def. 1). (Def. 1) There exist many sorted sets f , g indexed by N such that (i) n-BitSubtracterStr(x, y) = f(n), (ii) f(0) = 1GateCircStr(ε,Boolean 7−→ true), (iii) g(0) = 〈ε, Boolean 7−→ true〉, and (iv) for every natural number n and for every non empty many sorted signature S and for every set z such that S = f(n) and z = g(n) holds f(n + 1) = S+·BitSubtracterWithBorrowStr(x(n + 1), y(n + 1), z) and g(n + 1) = BorrowOutput(x(n + 1), y(n + 1), z). Let n be a natural number and let x, y be finite sequences. The functor n-BitSubtracterCirc(x, y) yielding a Boolean strict circuit of