Compositional Analysis of Dynamical Systems using Predicate Transformers (Summary).

Introduction We propose a complementary approach to discrete dynamical systems, using predicate transformers. We present general concepts like invariance and attraction, and we propose properties to characterize the structure of invariants. Then we present the concept of composition of dynamical systems. We define algebraic operators on systems and we try to discover how dynamical properties of small systems are preserved or transformed when these are composed into more complex systems. Finally, we illustrate this approach on an example. We work with a space E (e.g. N, or R), and extend functions from E to E into functions PE ! PE, which are invertible. Any subset of E can be described by a predicate. For example, an interval [a; b] ` R is defined by the predicate P (x)