Kolmogorov Complexity and Computational Complexity

Kolmogorov Complexity and Computational Complexity

In relation to computational complexity theory, resource-bounded Kolmogorov complexities are frequently considered. For example, the t(n)-time bounded Kolmogorov complexity of a string a is the size of the shortest string y from which ...

Author: Osamu Watanabe

Publisher: Springer Science & Business Media

ISBN: 9783642777356

Category: Computers

Page: 105

View: 179

The mathematical theory of computation has given rise to two important ap proaches to the informal notion of "complexity": Kolmogorov complexity, usu ally a complexity measure for a single object such as a string, a sequence etc., measures the amount of information necessary to describe the object. Compu tational complexity, usually a complexity measure for a set of objects, measures the compuational resources necessary to recognize or produce elements of the set. The relation between these two complexity measures has been considered for more than two decades, and may interesting and deep observations have been obtained. In March 1990, the Symposium on Theory and Application of Minimal Length Encoding was held at Stanford University as a part of the AAAI 1990 Spring Symposium Series. Some sessions of the symposium were dedicated to Kolmogorov complexity and its relations to the computational complexity the ory, and excellent expository talks were given there. Feeling that, due to the importance of the material, some way should be found to share these talks with researchers in the computer science community, I asked the speakers of those sessions to write survey papers based on their talks in the symposium. In response, five speakers from the sessions contributed the papers which appear in this book.
Categories: Computers

Applied and Computational Control Signals and Circuits

Applied and Computational Control  Signals  and Circuits

wonderful commonplace: to show that complexity, correctly viewed, is only a mask for simplicity. The field of computational complexity was later divided into two subfields: combinatorial complexity and information-based complexity [58].

Author: Biswa N. Datta

Publisher: Springer Science & Business Media

ISBN: 9781461205715

Category: Technology & Engineering

Page: 539

View: 469

The purpose of this annual series, Applied and Computational Control, Signals, and Circuits, is to keep abreast of the fast-paced developments in computational mathematics and scientific computing and their increasing use by researchers and engineers in control, signals, and circuits. The series is dedicated to fostering effective communication between mathematicians, computer scientists, computational scientists, software engineers, theorists, and practicing engineers. This interdisciplinary scope is meant to blend areas of mathematics (such as linear algebra, operator theory, and certain branches of analysis) and computational mathematics (numerical linear algebra, numerical differential equations, large scale and parallel matrix computations, numerical optimization) with control and systems theory, signal and image processing, and circuit analysis and design. The disciplines mentioned above have long enjoyed a natural synergy. There are distinguished journals in the fields of control and systems the ory, as well as signal processing and circuit theory, which publish high quality papers on mathematical and engineering aspects of these areas; however, articles on their computational and applications aspects appear only sporadically. At the same time, there has been tremendous recent growth and development of computational mathematics, scientific comput ing, and mathematical software, and the resulting sophisticated techniques are being gradually adapted by engineers, software designers, and other scientists to the needs of those applied disciplines.
Categories: Technology & Engineering

Computational Complexity

Computational Complexity

Proceedings : 18th IEEE Annual Conference on Computational Complexity : 7-10 July, 2003, Aarhus, Denmark IEEE Computer Society. Technical Committee on Mathematical Foundations of Computing. 6 Organization of the rest of the paper In ...

Author: IEEE Computer Society. Technical Committee on Mathematical Foundations of Computing

Publisher: Institute of Electrical & Electronics Engineers(IEEE)

ISBN: 0769518796

Category: Arhus, Denmark

Page: 387

View: 526

This is an annual conference that deals with computational complexity in very broad terms. Complexity 2003 looks into topics such as complexity classes, algebraic complexity, proof complexity, interactive proof systems, Kolmogorov complexity, Reducibility, communication complexity, complexity and logic, nonapproximability, cryptographic complexity, complexity and learning, quantum computation, circuits and other concrete computational models.
Categories: Arhus, Denmark

Computational Phenotypes

Computational Phenotypes

And here enters the theory of computational complexity. At the beginning of this appendix we saw that this theory is also concerned with sets, and we have just seen that it looks at sets as if they were problems in order to determine ...

Author: Sergio Balari

Publisher: Oxford University Press

ISBN: 9780199665464

Category: Language Arts & Disciplines

Page: 239

View: 252

This is a book about language as a species-typical trait of humans. It argues that language is not so exceptional after all, as according to the authors it is just the human version of a rather common and conservative organic system that they refer to as the Central Computational Complex.
Categories: Language Arts & Disciplines

Analytic Computational Complexity

Analytic Computational Complexity

Carnegie-Mellon University, Symposium on Analytic Computational Complexity Joseph Frederick Traub. THE COMPLEXITY OF OBTAINING STARTING POINTS FOR SOLVING OPERATOR EQUATIONS BY NEWTON'S METHOD H. T. Kung Department of Computer Science ...

Author: Carnegie-Mellon University


ISBN: UOM:39015006062502

Category: Computational complexity

Page: 239

View: 466

Categories: Computational complexity

Mathematical Principles of the Internet Two Volume Set

Mathematical Principles of the Internet  Two Volume Set

Therefore the multino6.7.2 Algorithmic-Complexity Classes This subsection is a brief tour of computational complexity of algorithms. This is a vast and deep subject in its own right. The computational complexity of an algorithm is a ...

Author: Nirdosh Bhatnagar

Publisher: CRC Press

ISBN: 9781351379212

Category: Computers

Page: 1768

View: 614

This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, these cover only a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.
Categories: Computers

QoS Management of Web Services

QoS Management of Web Services, the computational complexity of each similarity computation is 0(m). Therefore, the computational complexity of the similarity computation is 0(mn). After the similarity computation, for each missing value of an active Web ...

Author: Zibin Zheng

Publisher: Springer Science & Business Media

ISBN: 9783642342073

Category: Computers

Page: 150

View: 984

Quality-of-Service (QoS) is normally used to describe the non-functional characteristics of Web services and as a criterion for evaluating different Web services. QoS Management of Web Services presents a new distributed QoS evaluation framework for these services. Moreover, three QoS prediction methods and two methods for creating fault-tolerant Web services are also proposed in this book. It not only provides the latest research results, but also presents an excellent overview of QoS management of Web sciences, making it a valuable resource for researchers and graduate students in service computing. Zibin Zheng is an associate research fellow at the Shenzhen Research Institute, The Chinese University of Hong Kong, China. Professor Michael R. Lyu also works at the same institute.
Categories: Computers

Computer Networks

Computer Networks

2.4 Computational Complexity Analysis The computational complexity of algorithm in Fig. 1 is given by following equation: T(n)= (T1(ni,di )+T 2(ni,di )+T 3(ni,di)) + Tsort(n) (9) N∑ i=1 where N is the total number of quantum registers ...

Author: Andrzej Kwiecien

Publisher: Springer Science & Business Media

ISBN: 9783642026713

Category: Computers

Page: 353

View: 407

The continuous and very intense development of IT has resulted in the fast development of computer networks. Computer networks, as well as the entire ?eldofIT,aresubjectto constantchangestriggeredbythegeneraltechnological advancement and the in?uence of new IT technologies.These methods and tools of designing and modeling computer networks are becoming more advanced. Above all, the scope of their application is growing thanks to, for example, the results of new research and because of new proposals of application, which not long ago were not even taken into consideration. These new applications stimulate the development of scienti?c research, as the broader application of system solutions based on computer networks results in a wide range of both theoretical and practical problems. This book proves that and the contents of its chapters concern a variety of topics and issues. Generally speaking, the contents can be divided into several subject groups. The ?rst group of contributions concerns new technologies applied in computer networks,particularlythoserelatedto nano,molecularandquantumtechnology.
Categories: Computers

Computational Science and Its Applications ICCSA 2006

Computational Science and Its Applications   ICCSA 2006

In the Table 3, the reduction of computation complexity in percentage for 30Hz sequences is summarized for the cost function of Table 2. Also Table 4 corresponds to the 10Hz sequences. The absolute computation complexity can be affected ...

Author: Osvaldo Gervasi

Publisher: Springer

ISBN: 9783540340713

Category: Computers

Page: 1204

View: 574

The five-volume set LNCS 3980-3984 constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2006. The volumes present a total of 664 papers organized according to the five major conference themes: computational methods, algorithms and applications high performance technical computing and networks advanced and emerging applications geometric modelling, graphics and visualization information systems and information technologies. This is Part I.
Categories: Computers

Network Design

Network Design

In Table 2.5 , we summarize commonly used terminology describing computational complexity . The terms listed below are sorted from low to high complexity . In general , network design algorithms are considered efficient if they are of O ...

Author: Teresa C. Piliouras

Publisher: CRC Press

ISBN: 0849334047

Category: Computers

Page: 416

View: 580

Network Design outlines the fundamental principles and analytical techniques used in designing data networks. The text enables future managers and technical professionals to better understand and appreciate each other's perspective in the network design process. Network managers will need a sound grounding in basic design principles to effectively manage, plan, and assess the plethora of new technologies and equipment available for designing networks. They also must understand how requirements should be formulated and specified for design engineers. Similarly, network designers and engineers need a sound grounding in basic management principles to fully understand how organizational requirements best reflect design recommendations. Network Design enables network management and design professionals to work together toward achieving their respective goals in the network design process. It outlines basic techniques; reviews major challenges and issues; summarizes prevailing approaches and technologies; describes the specification, design, and planning data network topologies; and assesses specification and evaluation processes in designing and implementing data networks. This excellent, unique resource also : Emphasizes principles and analytical approaches that work independent of specific implementation of technology Includes case studies to illustrate how basic principles can be applied to realistic network design problems, considering both technical and management considerations Demystifies the design process, describing the lingua franca of both managers and design engineers in common terms Provides a better understanding of the total network design process
Categories: Computers