Defining structures through forbidding and enforcing constraints

This paper introduces a new way of modeling classes of physical and biochemical processes and structures based on boundary conditions that are called “forbidden” and “enforced”. The model of forbidding–enforcing systems (fe-systems) is presented in a general categorical sense and we use three specific examples of categories to illustrate three different phenomena. The hydrogen and covalent bonds of DNA, as well as splicing DNA by enzymes and recombination is illustrated with fe-systems on the category of languages (1-D structures). Fe-systems over the simple category of sets can define the solutions to a computational problem, the k-colorability problem (information processing). By using the category of graphs fe-systems model graphs as an abstraction of 3-D structures such that characterizations of familiar classes of graphs, such as trees, bi-partite graphs, and complete graphs are obtained.