Models of deterministic systems

Abstract

The definition of “model of a system” in terms of a homomorphism of the states of the system is evaluated and an alternative definition in terms of sequence generators is proposed. Sequence generators are finite graphs whose points represent complete states of a system. Sequence generators include finite automata and other information processing systems as special cases. It is shown how to define models in terms of a projection operator which applies to any sequence generator which has an output projection and yields a new sequence generator. A model produced by the projection operator is embedded in the system it models. The notion of embedding is discussed informally and some questions raised about the relations of deterministic, indeterministic, and probabilistic models and systems.