abstract compositional analysis iterated von geurts frederic (9 Ergebnisse)

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - State-transition systems model machines, programs, and speci cations [20, 23,284,329],butalsothegrowthanddeclineofantpopulations, nancial markets, diseases and crystals [22, 35, 178, 209, 279]. In the last decade, thegrowinguseofdigitalcontrollersinvariousenvironmentshasentailed theconvergenceofcontroltheoryandreal-timesystemstowardhybrids- tems [16] by combining both discrete-event facets of reality with Nature s continuous-time aspects. The computing scientist and the mathematician have re-discovered each other. Indeed, in the late sixties, the programming language Simula, father of modern object-oriented languages, had already been speci cally designed to model dynamical systems [76]. Today,theimportanceofcomputer-basedsystemsinbanks,telecom- nication systems, TVs, planes and cars results in larger and increasingly complex models. Two techniques had to be developed and are now fruitfully used to keep analytic and synthetic processes feasible: composition and - straction.Acompositionalapproachbuildssystemsbycomposingsubsystems that are smaller and more easily understood or built. Abstraction simpli es unimportantmattersandputstheemphasisoncrucialparametersofsystems. Inordertodealwiththecomplexityofsomestate-transitionsystemsand tobetterunderstandcomplexorchaoticphenomenaemergingoutofthe behaviorofsomedynamicalsystems,theaimofthismonographistopresent rststepstowardtheintegratedstudyofcompositionandabstractionin dynamical systems de ned by iterated relations. Themaininsightsandresultsofthisworkconcernastructuralorm f of complexityobtainedbycompositionofsimpleinteractingsystemspresenting opposedattractingbehaviors.Thiscomplexityexpressesitselfintheevo- tionofcomposedsystems,i.e.,theirdynamics,andintherelationsbetween their initial and nal states, i.e., the computations they realize. The theor- ical results presented in the monograph are then validated by the analysis ofdynamicalandcomputationalpropertiesoflow-dimensionalprototypesof chaotic systems (e.g. Smale horseshoe map, Cantor relation, logistic map), high-dimensional spatiotemporally complex systems (e.g. cellular automata), and formal systems (e.g. paperfoldings, Turing machines). Acknowledgements. ThismonographisarevisionofmyPhDthesiswhichwas completed at the Universit e catholique de Louvain (Belgium) in March 96. VIII Preface The results presented here have been in uenced by many people and I would like to take this opportunity to thank them all.

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Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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, Attractio.

Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -i.e., the computations they realize. The theor- ical results presented in the monograph are then validated by the analysis ofdynamicalandcomputationalpropertiesoflow-dimensionalprototypesof chaotic systems (e.g. Smale horseshoe map, Cantor relation, logistic map), high-dimensional spatiotemporally complex systems (e.g. cellular automata), and formal systems (e.g. paperfoldings, Turing machines). Acknowledgements. ThismonographisarevisionofmyPhDthesiswhichwas completed at the Universit¿ e catholique de Louvain (Belgium) in March 96. VIII Preface The results presented here have been in uenced by many people and I would like to take this opportunity to thank them all.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 292 pp. Englisch.

Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -State-transition systems model machines, programs, and speci cations [20, 23,284,329],butalsothegrowthanddeclineofantpopulations, nancial markets, diseases and crystals [22, 35, 178, 209, 279]. In the last decade, thegrowinguseofdigitalcontrollersinvariousenvironmentshasentailed theconvergenceofcontroltheoryandreal-timesystemstowardhybrids- tems [16] by combining both discrete-event facets of reality with Nature s continuous-time aspects. The computing scientist and the mathematician have re-discovered each other. Indeed, in the late sixties, the programming language Simula, father of modern object-oriented languages, had already been speci cally designed to model dynamical systems [76]. Today,theimportanceofcomputer-basedsystemsinbanks,telecom- nication systems, TVs, planes and cars results in larger and increasingly complex models. Two techniques had to be developed and are now fruitfully used to keep analytic and synthetic processes feasible: composition and - straction.Acompositionalapproachbuildssystemsbycomposingsubsystems that are smaller and more easily understood or built. Abstraction simpli es unimportantmattersandputstheemphasisoncrucialparametersofsystems. Inordertodealwiththecomplexityofsomestate-transitionsystemsand tobetterunderstandcomplexorchaoticphenomenaemergingoutofthe behaviorofsomedynamicalsystems,theaimofthismonographistoprese nt rststepstowardtheintegratedstudyofcompositionandabstractionin dynamical systems de ned by iterated relations. Themaininsightsandresultsofthisworkconcernastructuralorm f of complexityobtainedbycompositionofsimpleinteractingsystemspresenti ng opposedattractingbehaviors.Thiscomplexityexpressesitselfintheevo- tionofcomposedsystems,i.e.,theirdynamics,andintherelationsbetween their initial and nal states, i.e., the computations they realize. The theor- ical results presented in the monograph are then validated by the analysis ofdynamicalandcomputationalpropertiesoflow-dimensionalprototypesof chaotic systems (e.g. Smale horseshoe map, Cantor relation, logistic map), high-dimensional spatiotemporally complex systems (e.g. cellular automata), and formal systems (e.g. paperfoldings, Turing machines). Acknowledgements. ThismonographisarevisionofmyPhDthesiswhichwas completed at the Universit e catholique de Louvain (Belgium) in March 96. VIII Preface The results presented here have been in uenced by many people and I would like to take this opportunity to thank them all. 292 pp. Englisch.