Large Systems and their Regular Expressions: An Approach to Pattern Recognition

Systems theory deals with classes of identifiable parts each interacting in such a way that a given class exists together to satisfy certain specific requirements; these parts can be thought of an components of the system, some of which are permanent and some not. In analyzing a given system (see (13)) one usually offers up an m-tuple consisting of devices to be analyzed, pri-mitives to represent any device, allowable compositions , concepts of simulation, and theorems that tell how the devices are to be analyzed. Category theory serves as an organizational tool for large systems. Lerge a category with the category of sets is the category of functors whose morphisms are natural transformations between functors. We call a universe whose objects are node labels and whose morphisms are edge labels. Functor theory, having now reached a level of variety and depth in descriptive power , stands ready to help the systems theorist characterize those states which are important in the study of a particular system. A computer with a TV camera is a tissue scanner whose job is to verify homogeneity. That is, it detects flaws or holes in a tissue. It is well know that when two topological spaces are homeomorphic, then their fundamental groups are isomorphic. The job of the functor is to "record holes" in spaces. Zeeman'8 (38) concept of a tolerance space is useful when dealing with visual acuity, while Wallace's (35) concept of a separation space is helpful in recording the position of patterns.