Abstract compositional analysis of iterated relations : a structural approach to complex state transition systems

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

資料種別:: 図書
出版情報:: Berlin : Springer, c1998
形態:: xiv, 280 p. ; 24 cm
シリーズ名:: Lecture notes in computer science ; 1426 <BA00009279>
著者名:: Geurts, Frédéric
ISBN:: 9783540655060 [3540655069]
書誌ID:: BA39298855

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注記:

Includes bibliographical references (p. [257]-272) and index

主題:

Abstract data types; Electronic data processing--Structured techniques; System analysis

言語:

英語

目次情報:

Foreword / Michel Sintzoff

Preface

Prologue: Aims, Themes, and Motivations / 1：

Complex Relational Dynamical Systems / 1.1：

The Context: A First Contact with Dynamical Systems / 1.1.1：

Mutual Exclusion / 1.1.2：

Social Pressure / 1.1.3：

On the Chaotic Demography of Rabbits / 1.1.4：

Tools and Motivations / 1.2：

Overview of the Monograph / 1.3：

Mathematical Framework: Iterated Relations and Composition / Part I：

Dynamics of Relations / 2：

Functional Discrete-Time Dynamical Systems / 2.1：

Relational Dynamical Systems / 2.2：

Point-Level Nondeterministic Dynamics / 2.2.1：

Set-Level Deterministic Dynamics / 2.2.2：

Comparison / 2.2.3：

Preliminary Definitions and Properties / 2.3：

Basic Definitions About Relations / 2.3.1：

Notions from Topology / 2.3.2：

Monotonicity and General Junctivity Properties / 2.3.3：

Fixpoint Theorems / 2.3.4：

Elementary Properties / 2.3.5：

Metric Properties / 2.3.6：

Transfinite Iterations / 2.4：

Motivation / 2.4.1：

Transfinite Fixpoint Theorem / 2.4.2：

Transfinite Limits of Iterations / 2.4.3：

Discussion / 2.5：

Relations vs Functions / 2.5.1：

Set-Level Dynamics and Predicate-Transformers / 2.5.2：

Point-Level Dynamics and Trace Semantics / 2.5.3：

Nondeterminism and Probabilistic Choices / 2.5.4：

Time Structure / 2.5.5：

Dynamics of Composed Relations / 3：

Structural Composition / 3.1：

Composition of Relations / 3.2：

Unary Operators / 3.2.1：

N-Ary Operators / 3.2.2：

Composed Dynamical Systems / 3.2.3：

One-Step Set-Level Evolution of Composed Relations / 3.3：

Point-Level Dynamics of Composed Systems / 3.3.2：

Algebraic Properties of Composition Operators / 3.4：

Composition of Unary Operators / 3.4.1：

Composition of Unary and N-Ary Operators / 3.4.2：

Composition of N-Ary Operators / 3.4.3：

Fixpoint Theory for the Composition / 3.4.4：

Composition Operators / 3.5：

Nondeterminism and Probabilities Revisited / 3.5.2：

Fixpoint Operator and Composition / 3.5.3：

Abstract Complexity: Abstraction, Invariance, Attraction / Part II：

Abstract Observation of Dynamics / 4：

Observation of Systems / 4.1：

Trace-Based Dynamics / 4.2：

Symbolic Observation / 4.3：

Abstraction of Systems / 4.4：

Qualitative Abstract Verification / 4.5：

Observation as Abstraction / 4.6：

Observation and Abstraction: Related Work / 4.7：

Symbolic Dynamics vs Astract Observation / 4.7.2：

Invariance, Attraction, Complexity / 4.7.3：

Invariance / 5.1：

Forward and Backward Invariance / 5.1.1：

Global Invariance / 5.1.2：

Strong Invariance / 5.1.3：

Structure of Invariants / 5.2：

Trace-Parametrized Invariants / 5.2.1：

Fullness and Atomicity / 5.2.2：

Chaos / 5.2.3：

Fullness Implies Trace Chaos / 5.2.4：

Fullness and Atomicity Imply Knudsen Chaos / 5.2.5：

Devaney vs Trace vs Knudsen Chaos / 5.2.6：

Fullness and Atomicity Criteria / 5.3：

Criteria / 5.3.1：

Case Studies: Dyadic Map, Cantor Relation, Logistic Map / 5.3.2：

Attraction / 5.4：

Intuition: From Reachability to Attraction / 5.4.1：

From Weak to Full Attraction / 5.4.2：

A Taxonomy of Attraction / 5.4.3：

Attraction Criteria / 5.5：

Attraction by Invariants / 5.6：

Invariance and Attraction: Related Notions / 5.7：

Energy-Like Functions / 5.7.2：

Dynamical Complexity / 5.7.3：

Abstract Compositional Analysis of Systems: Dynamics and Computations / Part III：

Compositional Analysis of Dynamical Properties / 6：

Aims and Informal Results / 6.1：

Inversion / 6.2：

Restrictions / 6.3：

Domain Restriction / 6.3.1：

Range Restriction / 6.3.2：

Negation / 6.4：

Sequential Composition / 6.5：

Intersection / 6.6：

Union / 6.7：

Products / 6.8：

Free Product / 6.8.1：

Connected Product / 6.8.2：

Combining Union with Free Product / 6.9：

Compositionality: Summary / 6.10：

Limitations and Open Problems / 6.10.2：

Related Work / 6.10.3：

Emergence of Complexity by Structural Composition / 6.10.4：

Case Studies: Compositional Analysis of Dynamics / 7：

A Collection of Complex Behaviors / 7.1：

Smale Horseshoe Map / 7.2：

Cantor Relation / 7.3：

From Cantor Relation to Truncated Logistic Map / 7.4：

Paperfoldings / 7.5：

Introduction / 7.5.1：

Paperfolding Sequences / 7.5.2：

Dynamical Complexity of Paperfoldings / 7.5.3：

Partial Conclusions / 7.5.4：

Discussion: Compositional Dynamical Complexity / 7.6：

Experimental Compositional Analysis of Cellular Automata / 8：

Aims and Motivations: Attraction-Based Classification and Composition / 8.1：

Preliminary Notions / 8.2：

Cellular Automata / 8.2.1：

Transfinite Attraction / 8.2.2：

Shifted Hamming Distance / 8.2.3：

Experimental Classification / 8.3：

Formal Attraction-Based Classification / 8.4：

Type-<$>{\cal N}<$> Cellular Automata / 8.4.1：

Type-<$>{\cal F}<$> Cellular Automata / 8.4.3：

Type-<$>{\cal P}<$> Cellular Automata / 8.4.4：

Type-<$>{\cal S}<$> Cellular Automata / 8.4.5：

Type-<$>{\cal A}<$> Cellular Automata / 8.4.6：

Structural Organizations of CA Classes / 8.4.7：

Motivation: Simulation vs Theoretical Results / 8.5.1：

Linear Periodicity Hierarchy / 8.5.2：

Periodicity Clustering / 8.5.3：

Organization w.r.t. Shifted Hamming Distance / 8.5.4：

Dynamical Complexity in CA / 8.5.5：

Conjectures in CA Composition / 8.6：

Complexity by Composition of Shifts / 8.7：

Rules 2 and 16 / 8.7.1：

A More Precise Conjecture / 8.7.2：

Qualitative Analysis and Complexity Measures / 8.8：

Compositional Analysis of Complex CA / 8.9：

Local Disjunction, Local Union, and Global Union / 8.9.1：

Comparison and Summary of Results / 8.9.2：

Summary and Partial Conclusion / 8.10：

Open Questions / 8.10.2：

Classification: State-of-the-Art / 8.10.3：

Aperiodicity in Cellular Automata / 8.10.4：

Related Work in Composition / 8.10.5：

Compositional Analysis of Computational Properties / 9：

Automata as Dynamical Systems / 9.1：

Comparing Dynamical Systems / 9.2：

Extrinsic Method / 9.2.1：

Intrinsic Method / 9.2.2：

Our Comparison / 9.2.3：

From Locality to Globality / 9.3：

Turing Machines / 9.3.1：

Continuous Functions / 9.3.2：

General Model / 9.3.4：

Comparison Through Simulation / 9.4：

Simulation / 9.4.1：

Choice of Coding / 9.4.2：

From TM to CA / 9.4.3：

From CA to CF / 9.4.4：

Weak Hierarchy / 9.4.5：

Topological and Metric Properties / 9.5：

Continuity / 9.5.1：

Shift-Invariance / 9.5.2：

Lipschitz Property / 9.5.3：

Shift-Vanishing Effect / 9.5.4：

Nondeterminism / 9.5.5：

Summary / 9.5.6：

Computability of Initial Conditions / 9.6：

Hierarchy of Systems / 9.7：

Composition and Computation / 9.8：

Further Work / 9.8.2：

Epilogue: Conclusions and Directions for Future Work / 9.8.3：

Contributions and Related Work / 10.1：

Mathematical Framework / 10.1.1：

Compositional Analysis / 10.1.2：

Directions for Future Research / 10.2：

A Patchwork of Open Technical Issues / 10.2.1：

Fractal Image Compression / 10.2.2：

Distributed Dynamical Optimization / 10.2.3：

Distributed Systems and Self-Stabilization / 10.2.4：

Probabilistic Systems and Measures / 10.2.5：

Higher-Order Systems, Control, and Learning / 10.2.6：

Design of Attraction-Based Systems / 10.2.7：

The Garden of Structural Similarities / 10.3：

Coda: Compositional Complexity Revisited / 10.4：

Bibliography

Glossary of Symbols

Index

Foreword / Michel Sintzoff

Preface

Prologue: Aims, Themes, and Motivations / 1：

Complex Relational Dynamical Systems / 1.1：

The Context: A First Contact with Dynamical Systems / 1.1.1：

Mutual Exclusion / 1.1.2：

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