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The authors study a class of discrete dynamical systems that is motivated by the generic structure of simulations. The systems consist of the following data: (a) a finite graph Y with vertex set {l_brace}1, ..., n{r_brace} where each vertex has a binary state, (b) functions F{sub i}:F2??20--?? → F2??20--?? and (c) an update ordering?. The functions F{sub i} update the binary state of vertex i as a function of the state of vertex i and its Y-neighbors and leave the states of all other vertices fixed. The update ordering is a permutation of the Y-vertices. They derive a decomposition result, characterize invertible SDS and study fixed points. In particular they analyze how many different SDS that can be obtained by reordering a given multiset of update functions and give a criterion for when one can derive concentration results on this number. Finally, some specific SDS are investigated.
This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.
Computer simulation has developed into a powerful tool for problem solving in a variety of areas, in the sciences as well as in industrial environments. New developments such as parallel simulation techniques will further improve the efficiency of the tool. Decision support systems, either based on mathematical models or on knowledge based expert systems will make computer simulation accessible to more users, and will provide better environments for systems analysis, modeling and simulation. Systems Analysis and Simulation presents the papers accepted for the 3rd International Symposium for Systems Analysis and Simulation held in Berlin (GDR) in September of 1988. The contributions selected for this two-volume set present the state of the art and current trends in computer simulation. Volume I emphasizes the theoretical foundations and the methodology for computer simulation and systems analysis. Volume II presents a variety of applications in fields such as manufacturing, robotics, economics, and biology.
The subject of this paper is the development of mathematical foundations for a theory of simulation. Sequentially updated cellular automata (sCA) over arbitrary graphs are employed as a paradigmatic framework. In the development of the theory, the authors focus on the properties of causal dependencies among local mappings in a simulation. The main object of and study is the mapping between a graph representing the dependencies among entities of a simulation and a representing the equivalence classes of systems obtained by all possible updates.
Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
Many researchers from different countries converged at the 10th Italian Conference on Theoretical Computer Science (ICTCS 2007) to discuss recent developments in theoretical computer science. The volume contains all contributed papers selected for presentation with the invited lectures delivered. The subjects of this book range from logical and mathematical aspects of computing, design and analysis of algorithms, to semantics of programming languages. Sample Chapter(s). Part A: Invited Talks: Clairvoyance and Laziness for on Line Travelling Agents (27 KB). Contents: Clairvoyance and Laziness for on Line Travelling Agents (G Ausiello); Symmetries in Foundations (G Longo); On the Approximability of Dense Steiner Tree Problems (M Hauptmann); Analyzing Non-Inteference with Respect to Classes (D Zanardini); Modeling Fuzzy Behaviours in Concurrent Systems (L D''Errico & M Loreti); Sorting Streamed Multisets (T Gagie); Dichotomy Results for Fixed Point Counting in Boolean Dynamical Systems (S Kosub & C M Homan); Definable Sets in Weak Presburger Arithmetic (C Choffrut & A Frigeri); and other papers. Readership: Theoretical computer scientists.
The theory of modern dynamical systems dates back to 1890 with studies by Poincaré on celestial mechanics. The tradition was continued by Birkhoff in the United States with his pivotal work on periodic orbits, and by the Moscow School in Russia (Liapunov, Andronov, Pontryagin). In the 1960s the field was revived by the emergence of the theory of chaotic attractors, and in modern years by accurate computer simulations. This book provides an overview of recent developments in the theory of dynamical systems, presenting some significant advances in the definition of new models, computer algorithms, and applications. Researchers, engineers and graduate students in both pure and applied mathematics will benefit from the chapters collected in this volume.
This book constitutes the refereed proceedings of the 4th International Conference on Unconventional Computation, UC 2005, held in Sevilla, Spain in September 2005. The conference formerly was named Unconventional Models of Computation (UMC). The 19 revised full papers presented together with 5 invited full papers were carefully reviewed and selected for inclusion in the book. All major areas of unconventional computing models are covered in theory as well as in experiments and applications. Topics addressed are: natural computing including quantum, cellular, molecular, neural and evolutionary computing; chaos and dynamical systems based computing; and various proposals for computations that go beyond the Turing model.
An introduction to certain aspects of developments in the modern theory of dynamics and simulation for a wide audience of scientifically literate readers. Unlike general texts on chaos theory and dynamical systems theory, this book follows the work on a specific problem at the very beginning of the modern era of dynamics, from its inception in 1954 through the early 1970s. It discusses such problems as the nonlinear oscillator simulation, the seminal discoveries at MIT in the early 1950s, the mathematical rediscovery of solitons in the late 1950s and the general problems of computability. In following these developments, the initial development of many of the now standard techniques of nonlinear modelling and numerical simulation are seen. No other text focuses so tightly and covers so completely one specific, pernicious problem at the heart of dynamics.