Abstract Compositional Analysis of Iterated Relations : A Structural Approach to Complex State Transition Systems
Language: English
Published by Springer, Berlin, Springer, 1998
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Add to basketItem description from seller
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,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. …
Seller Inventory # 9783540655060
- Title
- Abstract Compositional Analysis of Iterated Relations : A Structural Approach to Complex State Transition Systems
- Author
- Frederic Geurts
- Publisher
- Springer, Berlin, Springer
- Publication year
- 1998
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 3540655069
- ISBN 13
- 9783540655060
- Item weight
- 446 grams
- Dimensions
- 236x156x16 mm
"Synopsis" may belong to another edition of this title.
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