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Compositional Analysis of Iterated Relations: Dynamics and Computations

by Geurts, Frédéric

Abstract (Summary)
Discrete-time relational dynamical systems are mathematical models of possibly nonlinear and nondeterministic, state-based transition systems. They describe the time evolution of forests, viruses, parallel programs or cooperating agents. This thesis develops the compositional analysis of iterated relations: we study dynamical and computational properties of composed systems by combining the individual analyses of their components, simplified by abstraction techniques. We present a structural view of dynamical complexity, and a strict computational hierarchy of systems. Classical case studies are successfully analyzed: low-dimensional chaotic systems (logistic map, Smale horseshoe map, Cantor relation), high-dimensional complex systems (cellular automata), as well as formal systems (paperfoldings, Turing machines).
Bibliographical Information:

Advisor:

School:Université catholique de Louvain

School Location:Belgium

Source Type:Master's Thesis

Keywords:iterated relations

ISBN:

Date of Publication:03/22/1997

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