The algorithm for the minimization operator μ"y'y") will, in essence, create a sequence of instances of the function φ(x, "y") as the value of parameter "y" (a natural number) increases; the process will continue (see Note † below) until a match occurs between the output of function φ(x, "y") and some pre-established number (usually 0). Thus the evaluation of φ(x, "y") requires, at the outset, assignment of a natural number to each of its variables x"' and an assignment of a "match-number" (usually 0) to a register ""w"", and a number (usually 0) to register "y".