Abstract Compositional Analysis of Iterated Relations: A Structural Approach to Complex State Transition Systems: v. 1426 by Fraedaeric Geurts (Paperback, 1998)
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- DescriptionState-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  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 . 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 w 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. Irdertodealwiththecomplexityofsomestate-transitionsystemsand tobetterunderstandcomplexorchaoticphemenaemergingoutofthe behaviorofsomedynamicalsystems,theaimofthismographistopresent ?rststepstowardtheintegratedstudyofcompositionandabstractionin dynamical systems de?ned by iterated relations. Themaininsightsandresultsofthisworkconcernastructuralorm f of complexityobtainedbycompositiofsimpleinteractingsystemspresenting opposedattractingbehaviors.Thiscomplexityexpressesitselfintheevo- tiofcomposedsystems,i.e.,theirdynamics,andintherelationsbetween their initial and ?nal states, i.e., the computations they realize. The theor- ical results presented in the mograph 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). Ackwledgements. ThismographisarevisiofmyPhDthesiswhichwas 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.
- Author(s)Fraedaeric Geurts
- PublisherSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Date of Publication18/12/1998
- SubjectComputing: Professional & Programming
- Series TitleLecture Notes in Computer Science
- Series Part/Volume Number1426
- Place of PublicationBerlin
- Country of PublicationGermany
- ImprintSpringer-Verlag Berlin and Heidelberg GmbH & Co. K
- Content Notebiography
- Weight450 g
- Width155 mm
- Height235 mm
- Spine15 mm
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