Some Classical Mathematical Results Related to the Problems of the Firmware/Hardware Interface

The paper reviews the Shannon and Reed-Muller Decomposition Theorems and notes the relationship of the former to machine instruction set. It hypothesizes an instruction set based on Galois field operations and applies the divided difference methods of Newton to the automatic generation of a polynomial representation of an arbitrary function. Some numeric results are given for the fields GF(9) and GF(16). An extension of the methods to the representation of functions by rational forms is suggested.