The Counter machine's reference model is a set of choices and conventions to be used with the Counter machine and other model variants of the Register machine concept. It permits comparisons between models, and serves a didactic function with regards to examples and descriptions.
Contents
It is based on conventional models, labels and terminology. The reference (base) model is intended to preserve consistency between articles.
Introduction
In counter machine models the reader will observe, and may be bewildered by, the plethora of instruction sets defined by their authors. This reference will use the symbolism defined below to provide a standarized presentation format (syntax) to facilitate comparison of the sets and help give them definition.
The base model is derived from Minsky (1967), Lambek (1961) and in particular Shepherdson-Sturgis (1963 p. 225).
Formal Definition
The Counter machine reference model consists of a finite set of registers r1 ... rn, each of which can hold a non-negative integer, r0 (always zero), and a finite list of instructions I1 ... Im. Each of the instructions in this list is one of the following:
INC(j) — increment the value of register rj by 1; go to the successor instruction (e.g. instruction that is numerically next-in-sequence).DEC(j) — If the contents of r is not 0 (not empty) then decrement the value of register rj by 1, else the contents of r=0; go to the successor instruction.JZ (j, z) — If the contents of register rj equals Zero then Jump to instruction Iz else go to the successor instruction.HALT — halts the computation.Formal Semantic: