A theory of closure operators

Abstract

We explore how fixed-point operators can be designed to interact and be composed to form autonomic control mechanisms. We depart from the idea that an operator is idempotent only for the states that it assures, and define a more general concept in which acceptable states are a superset of assurable states. This modified definition permits operators to make arbitrary choices that are later changed by other operators, easing their composition and allowing them to maintain aspects of a configuration. The result is that operators can be used to implement closures, which can in turn be used to build self-managing systems. © 2008 Springer-Verlag Berlin Heidelberg.