Duo-Internal Labeled Graphs with Distinguished Nodes : a Categorial Framework for Graph Based Anticipatory Systems

A categorial framework for structured graph based systems with or without distinguished nodes or labeling on both arcs and nodes is proposed. Requirements for the existence of limits and colimits in the resulting categories are set. In this context, unrestricted and bicomplete categories of graph based systems such as Petri Nets, Labeled Transition Systems, Nonsequential Automata, etc., are easily defined. Then it is shown how limits and colimits can be interpreted as structuring and anticipatory properties of systems. The proposed framework called duo-internalization generalizes the notion of intemal graphs allowing that nodes and arc may be objects from different categories. The results about limits and colimits of (reflexive) duo-intemal (labeled) graphs (with distinguished nodes) are, for our knowledge, new.