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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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.
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.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
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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. Bestandsnummer des Verkäufers 9783540655060
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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. Bestandsnummer des Verkäufers 9783540655060
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