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)

Analysis of Dynamical Systems using Predicate Transformers: Attraction and Composition

. We present a framework for the compositional analysis of dynamical systems. This framework is based on set-valued functions, defined by predicate transformers. It integrates concepts from mathematics, computing science, and neurosciences. We also introduce an additional concept: the attraction between predicates. The main results of the paper are then presented. We propose composition rules which permit to see a complex system as composed of simpler ones, to study these simple systems using the concepts introduced before, and then to compose the results for deriving the analysis of the initial complex system. 1 Introduction Discrete autonomous dynamical systems [1, 2] can be analyzed using predicate transformers for iterated guarded commands [3]. Initial results of such a study have been reported [4]; they provide sufficient criteria on invariants of infinite iterations for detecting topological transitivity and sensitive dependence on initial conditions. The present paper tackles t..

The Composition

The main features of Algol 68 are explained from a semantic point of view. It is shown how the language permits the composition of values and actions, i.e. ultimately programs, from a minimum set of primitives with a few fundamental recursive rules of composition. The associated syntax is briefly reviewed. An attempt has been made to obtain a structured and simple introduction to both Algol 68 and its orthogonal desgn. Key Words and Phrases: programming primitivies, programming languages, Algol, semantics, recursive composition, design of programming languages, data structure

Aide à la Reconnaissance et à l’Interprétation de l’Occupation du Sol – ARIOS

Projet de recherche dans le cadre de la 4ème phase du programme TELSATinfo:eu-repo/semantics/publishe