| Abstract Compositional Analysis of Iterated Relations: A Structural Approach to Complex State Transition Systems 1998 Edition Contributor(s): Geurts, Frederic (Author) |
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ISBN: 3540655069 ISBN-13: 9783540655060 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: December 1998 |
| Additional Information |
| BISAC Categories: - Computers | Data Modeling & Design - Medical - Computers | Computer Science |
| Dewey: 005.73 |
| LCCN: 99010039 |
| Series: Lecture Notes in Computer Science, |
| Physical Information: 0.61" H x 6.14" W x 9.21" (0.91 lbs) 280 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. 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. |