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• catalog abstract "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.".
• catalog contributor b11217509.
• catalog created "c1998.".
• catalog date "1998".
• catalog date "c1998.".
• catalog dateCopyrighted "c1998.".
• catalog description "Includes bibliographical references (p. [257]-272) and index.".
• catalog description "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.".
• catalog description "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. ".
• catalog description "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.".
• catalog description "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. ".
• catalog extent "xiv, 280 p. :".
• catalog hasFormat "Abstract compositional analysis of iterated relations.".
• catalog identifier "3540655069 (pbk. : alk. paper)".
• catalog isFormatOf "Abstract compositional analysis of iterated relations.".
• catalog isPartOf "Lecture notes in computer science, 0302-9743 ; 1426".
• catalog issued "1998".
• catalog issued "c1998.".
• catalog language "eng".
• catalog publisher "Berlin ; New York : Springer,".
• catalog relation "Abstract compositional analysis of iterated relations.".
• catalog subject "005.7/3 21".
• catalog subject "Abstract data types (Computer science)".
• catalog subject "Computer science.".
• catalog subject "Electronic data processing Structured techniques.".
• catalog subject "Logic design.".
• catalog subject "QA76.9.A23 G48 1998".
• catalog subject "Software engineering.".
• catalog subject "System analysis.".
• catalog tableOfContents "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.".
• catalog title "Abstract compositional analysis of iterated relations : a structural approach to complex state transition systems / Frédéric Geurts.".
• catalog type "text".