In essence, this thesis presents a system closely related to the concept of Turing machines, wherein the output of a Turing machine, or a portion of the output of a Turing machine, is compactly represented as a production. This thesis develops the concept of treating particular occurrences of words produced by Turing machines as components of production. These productions are treated as elements of combinatorial systems. The recursive unsolvability of the word problems for such systems is established. Certain relations between such systems and the set of real numbers are noted, but not extensively investigated. It is shown that such systems form cancellation semi-groups, and provide an example of a cancellation semi-group not entirely composed of words for which the word problem is recursively unsolvable. Some suggestions for further work are mentioned at the end of the thesis.
