Download or read book Analysis Problems for Sequential Dynamical Systems and Communicating State Machines written by and published by . This book was released on 2001 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: A simple sequential dynamical system (SDS) is a triple (G, F, [pi]), where (i) G(V, E) is an undirected graph with n nodes with each node having a 1-bit state, (ii) F = [f1, f2 ..., f{sub n}] is a set of local transition functions with f{sub i} denoting a Boolean function associated with node Vv{sub i} and (iii) [pi] is a fixed permutation of (i.e., a total order on) the nodes in V.A single SDS transition is obtained by updating the states of the nodes in V by evaluating the function associated with each of them in the order given by [pi]. Such a (finite) SDS is a mathematical abstraction of simulation systems [BMR99, BR99]. In this paper, we characterize the computational complexity of determining several phase space properties of SDSs. The properties considered are t-REACHABILITY ('Can a given SDS starting from configuration I reach configuration B in t or fewer transitions?'), REACHABILITY('Can a given SDS starting from configuration I ever reach configuration B?') and FIXED POINT REACHABILITY ('Can a given SDS starting from configuration I ever reach configuration in which it stays for ever?'). Our main result is a sharp dichotomy between classes of SDSs whose behavior is 'easy' to predict and those whose behavior is 'hard' to predict. Specifically, we show the following. (1) The t-REACHABILITY, REACHABILITY and the FIXED POINT REACHABILITY problems for SDSs are PSPACE-complete, even when restricted to graphs of bounded bandwidth (and hence of bounded pathwidth and treewidth) and when the function associated with each node is symmetric. The result holds even for regular graphs of constant degree where all the nodes compute the same symmetric Boolean function. (2) In contrast, the t-REACHABILITYm REACHABILITY and FIXED POINT REACHABILITY problems are solvable in polynomial time for SDSs when the Boolean function associated with each node is symmetric and monotone. Two important consequences of our results are the following: (i) The close correspondence between SDSs and cellular automata (CA), in conjunctio with our lower bounds for SDSs, yields stronger lower bounds on the complexity of reachability problems for CA than known previously. (ii) REACHABILITY problems for hierarchically-specified linearly inter-connected copies of a single finite automaton are EXPSPACE-hard. The results can be combined with our related results to show hardness of a number of equivalence relations for such automata. The results can also be used to demonstrate that determining the sensitivity to initial conditions of such automata (as proposed in [Mo90, BPT91]) is computationally intractable.
Download or read book Mathematical Foundations of Computer Science 2001 written by Jiri Sgall and published by Springer. This book was released on 2003-08-06 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science, MFCS 2001, held in Marianske Lazne, Czech Republic in August 2001. The 51 revised full papers presented together with 10 invited contributions were carefully reviewed and selected from a total of 118 submissions. All current aspects of theoretical computer science are addressed ranging from mathematical logic and programming theory to algorithms, discrete mathematics, and complexity theory. Besides classical issues, modern topics like quantum computing are discussed as well.
Download or read book Fundamental Problems in Computing written by Sekharipuram S. Ravi and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Not applicable for bookstore catalogue
Download or read book Complexity of Analysis and Verification Problems for Communicating Automata and Discrete Dynamical Systems written by and published by . This book was released on 2001 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We identify several simple but powerful concepts, techniques, and results; and we use them to characterize the complexities of a number of basic problems II, that arise in the analysis and verification of the following models M of communicating automata and discrete dynamical systems: systems of communicating automata including both finite and infinite cellular automata, transition systems, discrete dynamical systems, and succinctly-specified finite automata. These concepts, techniques, and results are centered on the following: (1) reductions Of STATE-REACHABILITY problems, especially for very simple systems of communicating copies of a single simple finite automaton, (2) reductions of generalized CNF satisfiability problems [Sc78], especially to very simple communicating systems of copies of a few basic acyclic finite sequential machines, and (3) reductions of the EMPTINESS and EMPTINESS-OF-INTERSECTION problems, for several kinds of regular set descriptors. For systems of communicating automata and transition systems, the problems studied include: all equivalence relations and simulation preorders in the Linear-time/Branching-time hierarchies of equivalence relations and simulation preorders of [vG90, vG93], both without and with the hiding abstraction. For discrete dynamical systems, the problems studied include the INITIAL and BOUNDARY VALUE PROBLEMS (denoted IVPs and BVPs, respectively), for nonlinear difference equations over many different algebraic structures, e.g. all unitary rings, all finite unitary semirings, and all lattices. For succinctly specified finite automata, the problems studied also include the several problems studied in [AY98], e.g. the EMPTINESS, EMPTINESS-OF-INTERSECTION, EQUIVALENCE and CONTAINMENT problems. The concepts, techniques, and results presented unify and significantly extend many of the known results in the literature, e.g. [Wo86, Gu89, BPT91, GM92, Ra92, HT94, SH+96, AY98, AKY99, RH93, SM73, Hu73, HRS76, HR78], for communicating automata including both finite and infinite cellular automata and for finite automata specified by special kinds of context-free grammars, by regular operations augmented with squaring and intersection, and specified succinctly as in [AY98, AKY99]. Moreover, our development of these concepts, techniques, and results shows how several ideas, techniques, and results, for the individual models M above can be extended to apply to all or to most of these models. As one example of this and paraphrasing [BPTBl], we show that most of these models M exhibit computationally-intractable sensitive dependence on initial conditions, for the same reason. These computationally-intractable sensitivities range from PSPACE-hard to undecidable.
Download or read book Mathematical Foundations of Computer Science written by and published by . This book was released on 2001 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Sequential Dynamical Systems written by Henning Mortveit and published by Springer Science & Business Media. This book was released on 2007-11-27 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book NBS Special Publication written by and published by . This book was released on 1965 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Systems Analysis and Design written by Alan Dennis and published by John Wiley & Sons. This book was released on 2015-03-02 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems Analysis and Design: An Object-Oriented Approach with UML, 5th Edition by Dennis, Wixom, and Tegarden captures the dynamic aspects of the field by keeping students focused on doing SAD while presenting the core set of skills that every systems analyst needs to know today and in the future. The text enables students to do SAD—not just read about it, but understand the issues so they can actually analyze and design systems. The text introduces each major technique, explains what it is, explains how to do it, presents an example, and provides opportunities for students to practice before they do it for real in a project. After reading each chapter, the student will be able to perform that step in the system development process.
Download or read book Discrete Event Systems Manufacturing Systems and Communication Networks written by P.R. Kumar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications DISCRETE EVENT SYSTEMS, MANUFACTURING SYSTEMS AND COMMUNICATION NETWORKS is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory. " The study of discrete event dynamical systems (DEDS) has become rapidly popular among researchers in systems and control, in communication networks, in manufacturing, and in distributed computing. This development has created problems for re searchers and potential "consumers" of the research. The first problem is the veritable Babel of languages, formalisms, and approaches, which makes it very difficult to determine the commonalities and distinctions among the competing schools of approaches. The second, related, problem arises from the different traditions, paradigms, values, and experience that scholars bring to their study of DEDS, depending on whether they come from control, com munication, computer science, or mathematical logic. As a result, intellectual exchange among scholars becomes compromised by unexplicated assumptions. The purpose of the Workshop was to promote exchange among scholars representing some of the major "schools" of thought in DEDS with the hope that (1) greater clarity will be achieved thereby, and (2) cross-fertilization will lead to more fruitful questions. We thank P. R. Kumar and P. P. Varaiya for organizing the workshop and editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr.
Download or read book Simulation and Optimization written by Georg Pflug and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers presented at the "International Workshop on Computationally Intensive Methods in Simulation and Op th th timization" held from 23 to 25 August 1990 at the International Institute for Applied Systems Analysis (nASA) in La~enburg, Austria. The purpose of this workshop was to evaluate and to compare recently developed methods dealing with optimization in uncertain environments. It is one of the nASA's activities to study optimal decisions for uncertain systems and to make the result usable in economic, financial, ecological and resource planning. Over 40 participants from 12 different countries contributed to the success of the workshop, 12 papers were selected for this volume. Prof. A. Kurzhanskii Chairman of the Systems and Decision Sciences Program nASA Preface Optimization in an random environment has become an important branch of Applied Mathematics and Operations Research. It deals with optimal de cisions when only incomplete information of t.he future is available. Consider the following example: you have to make the decision about the amount of production although the future demand is unknown. If the size of the de mand can be described by a probability distribution, the problem is called a stochastic optimization problem.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Predecessor and Permutation Existence Problems for Sequential Dynamical Systems written by and published by . This book was released on 2001 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book College of Engineering written by University of Michigan. College of Engineering and published by UM Libraries. This book was released on 1995 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book OAR written by and published by . This book was released on 1967 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book University of Michigan Official Publication written by University of Michigan and published by UM Libraries. This book was released on 1993 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each number is the catalogue of a specific school or college of the University.
Download or read book National Bureau of Standards Miscellaneous Publication written by and published by . This book was released on 1965 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Air Force Research Resum s written by and published by . This book was released on with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
