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Abstract compositional analysis of iterated relations : a structural approach to complex state transition systems / Frédéric Geurts.

By: Material type: TextTextSeries: Lecture notes in computer science ; 1426.Publication details: Berlin ; New York : Springer, ©1998.Description: 1 online resource (xiv, 280 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540492115
  • 3540492119
Subject(s): Additional physical formats: Print version:: Abstract compositional analysis of iterated relations.DDC classification:
  • 005.7/3 21
LOC classification:
  • QA76.9.A23 G48 1998
Other classification:
  • 54.10
  • SS 4800
  • 28
  • DAT 510f
Online resources:
Contents:
Prologue: Aims, Themes, and Motivations -- Prologue: Aims, Themes, and Motivations -- Mathematical Framework: Iterated Relations and Composition -- Dynamics of Relations -- Dynamics of Composed Relations -- Abstract Complexity: Abstraction, Invariance, Attraction -- Abstract Observation of Dynamics -- Invariance, Attraction, Complexity -- Abstract Compositional Analysis of Systems: Dynamics and Computations -- Compositional Analysis of Dynamical Properties -- Case Studies: Compositional Analysis of Dynamics -- Experimental Compositional Analysis of Cellular Automata -- Compositional Analysis of Computational Properties -- Epilogue: Conclusions and Directions for Future Work.
Action note:
  • digitized 2010 HathiTrust Digital Library committed to preserve
Summary: This self-contained monograph is an integrated study of generic systems defined by iterated relations using the two paradigms of abstraction and composition. This accommodates the complexity of some state-transition systems and improves understanding of complex or chaotic phenomena emerging in some dynamical systems. The main insights and results of this work concern a structural form of complexity obtained by composition of simple interacting systems representing opposed attracting behaviors. This complexity is expressed in the evolution of composed systems (their dynamics) and in the relations between their initial and final states (the computation they realize). The theoretical results are validated by analyzing dynamical and computational properties of low-dimensional prototypes of chaotic systems, high-dimensional spatiotemporally complex systems, and formal systems.
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Includes bibliographical references (pages 257-272) and index.

This self-contained monograph is an integrated study of generic systems defined by iterated relations using the two paradigms of abstraction and composition. This accommodates the complexity of some state-transition systems and improves understanding of complex or chaotic phenomena emerging in some dynamical systems. The main insights and results of this work concern a structural form of complexity obtained by composition of simple interacting systems representing opposed attracting behaviors. This complexity is expressed in the evolution of composed systems (their dynamics) and in the relations between their initial and final states (the computation they realize). The theoretical results are validated by analyzing dynamical and computational properties of low-dimensional prototypes of chaotic systems, high-dimensional spatiotemporally complex systems, and formal systems.

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Print version record.

Prologue: Aims, Themes, and Motivations -- Prologue: Aims, Themes, and Motivations -- Mathematical Framework: Iterated Relations and Composition -- Dynamics of Relations -- Dynamics of Composed Relations -- Abstract Complexity: Abstraction, Invariance, Attraction -- Abstract Observation of Dynamics -- Invariance, Attraction, Complexity -- Abstract Compositional Analysis of Systems: Dynamics and Computations -- Compositional Analysis of Dynamical Properties -- Case Studies: Compositional Analysis of Dynamics -- Experimental Compositional Analysis of Cellular Automata -- Compositional Analysis of Computational Properties -- Epilogue: Conclusions and Directions for Future Work.

English.

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