Toward a Formal Theory of Modeling and Simulation

Abstract

A simulation consists of a triple of automata (system to be simulated, model of this system, computer realizing the model). In a valid simulation these elements are connected by behavior and structure preserving morphisms. Informational and complexity considerations motivate the development of structure preserving morphisms which can preserve not only global, but also local dynamic structure. A formalism for automaton structure assignment and the relevant weak and strong structure preserving morphisms are introduced. It is shown that these preservation notions properly refine the usual automaton homomorphism concepts. Sufficient conditions are given under which preservation of the local state space structure (weak morphism) also forces the preservation of component interaction. The strong sense in which these conditions are necessary is also demonstrated. This provides a rationale for making valid inferences about the local structure of a system when that of a behaviorally valid model is known.