Symbolic synthesis of digital computers

In an ideal sense a binary digital computer or what might be called more generally a Boolean* machine is an automatic operational filing system. It is a machine which accepts information automatically in the form of words constructed from an alphabet of only two symbols, say 0 and 1, the so-called binary coded words. For example a binary number is such a word. This information is stored or recorded in sets of elementary boxes or files, each containing one of the symbols 0 or 1. This information is either transformed or used to change other files or itself as a function of the past contents of all files within the system. If the contents of all files within the system are constrained to change only at discrete points of time, say the points n (n = 1,2,3, ...), then the machine may be termed a synchronous Boolean machine. The discussion in this paper will be restricted to the synchronous Boolean machine.

It is evident from the above discussion that the content of each elementary box or file within the system is a two valued function, say A(t), of the real parameter time, t. Since the content of each file is constrained to change only at the discrete points of time n?, then a suitable definition for A(t) is the following: Either A(t) = 0 or A(t) = 1 for n? = t < (n+l)? where (n = 0 1,2, ...). In this definition the right continuity of A(t) has been assumed for the sake of definiteness. Let the function A(t) be called a file function.