Syntactic and semantic information in finite systems WŁODZISŁAW DUCH ABSTRACT A new measure of complexity or information content for finite systems is proposed. For systems composed from a number of interacting substructures the size of the minimal graph representing all possible structures is taken as its complexity. This type of complexity measure may also be used in a knowledge-based system to measure the semantic information. An algorithm for finding the minimal graph is given. Examples of applications include complex systems such as genes, proteins, language dictionaries and games. UMK-KMK-Technical Report-1-1993 1. Introduction: information and complex systems What is a complex system? A working definition, given at a recent conference on the subject [1], is: “... systems that exhibit complicated behavior but for which there is some hope that the underlying structure is simple in the sense of being governed by a small number of degrees of freedom”. Another definition recently given is: “A system is loosely defined as complex if it is composed of a large number of elements, interacting with each other, and the emergent global dynamics is qualitatively different from the dynamics of each one of the parts” [2]. Fractals and cellular automata are perhaps the simplest systems, in which almost infinite complexity is generated from extremely simple dynamics. In many-body physics few-body structures cannot be analyzed in details using mathematical models and may exhibit complex behavior. On the other hand this definition seems to be too restrictive. What about those complex systems for which there is no simple underlying structure? There are complex physical structures, like proteins and other biomolecules, which cannot be analyzed using theoretical methods of quantum mechanics because they are too complicated - the number of degrees of freedom is certainly not small. The size may not be that important. Large molecular aggregates, like crystals, may have high degree of symmetry which simplifies theoretical Department of Computer Methods Nicolaus Copernicus University Grudziądzka 5, 87-100 Toruń, Poland