Classical and New Paradigms of Computation and their Complexity Hierarchies

Classical and New Paradigms of Computation and their Complexity Hierarchies Papers of the conference “Foundations of the Formal Sciences III” held in Vienna, September 21-24, 2001 Complexity hierarchies derived from reduction functions ...

Author: Benedikt Löwe

Publisher: Springer Science & Business Media

ISBN: 1402027761

Category: Computers

Page: 260

View: 534

The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies. This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.

Classical and New Paradigms of Computation and Their Complexity Hierarchies

Author: Benedikt Lowe

Publisher:

ISBN: 9789401750950

Category:

Page: 276

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New Computational Paradigms

Classical and New Paradigms of Computation and their Complexity hierarchies, Papers of the Conference Foundations of the Formal Sciences III. Volume 23 of Trends in logic., Kluwer (2004) 8. Hamkins, J.D., Seabold, D.: Infinite time ...

Author: Barry S. Cooper

Publisher: Springer Science & Business Media

ISBN: 3540261796

Category: Computers

Page: 574

View: 398

This book constitutes the refereed proceedings of the first International Conference on Computability in Europe, CiE 2005, held in Amsterdam, The Netherlands in June 2005. The 68 revised full papers presented were carefully reviewed and selected from 144 submissions. Among them are papers corresponding to two tutorials, six plenary talks and papers of six special sessions involving mathematical logic and computer science at the same time as offering the methodological foundations for models of computation. The papers address many aspects of computability in Europe with a special focus on new computational paradigms. These include first of all connections between computation and physical systems (e.g., quantum and analog computation, neural nets, molecular computation), but also cover new perspectives on models of computation arising from basic research in mathematical logic and theoretical computer science.

A Primer on Quantum Computing

Cambridge University Press, New York (2013) Ambainis, A.: Quantum query algorithms and lower bounds. In: Löwe, B., Piwinger, B., Räsch, T. (eds.) Classical and New Paradigms of Computation and their Complexity Hierarchies, pp. 15–32.

Author: Franklin de Lima Marquezino

Publisher: Springer

ISBN: 3030190668

Category: Computers

Page: 109

View: 472

This book is about quantum computing and quantum algorithms. The book starts with a chapter introducing the basic rules of quantum mechanics and how they can be used to build quantum circuits and perform computations. Further, Grover's algorithm is presented for unstructured search discussing its consequences and applications. Next, important techniques are discussed such as Quantum Fourier Transform and quantum phase estimation. Finally, Shor's algorithm for integer factorization is explained. At last, quantum walks are explained in detail covering both the discrete and continuous time models,and applications of this techniques are described for the design and analyses of quantum algorithms.

Ordinal Computability

Classical and New Paradigms of Computation and their Complexity hierarchies, Papers of the Conference Foundations of the Formal Sciences III. Trends in Logic, vol. 23. Kluwer, Dordrecht, pp.223–237 (2001). Revision Theory.

Author: Merlin Carl

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110496151

Category: Mathematics

Page: 343

View: 694

Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.

Mathematical Foundations of Computer Science 2005

In Proceedings of the 16th IEEE Conference on Computational Complexity, pages 210–217, 2001. 2. ... In Classical and New Paradigms of Computation and their Complexity Hierarchies, Papers of the conference “Foundations of the Formal ...

Author: Joanna Jedrzejowicz

Publisher: Springer

ISBN: 3540318674

Category: Computers

Page: 814

View: 670

This volume contains the papers presented at the 30th Symposium on Mathematical Foundations of Computer Science (MFCS 2005) held in Gdansk, Poland from August 29th to September 2nd, 2005.

Logical Approaches to Computational Barriers

Hamkins and Welch have noticed [HaWe03, Theorem 1.7] that in general, nondeterministic Hamkins-Kidder computation can be more ... Classical and New Paradigms of Computation and their Complexity Hierarchies, Papers of the conference ...

Author: Arnold Beckmann

Publisher: Springer

ISBN: 3540354689

Category: Computers

Page: 608

View: 524

This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.

Models of Computation in Context

Classical and new paradigms of computation and their complexity hierarchies. Papers from the Conference Foundations of the Formal Sciences III (FotFS III) held at the Universität Wien, Vienna, September 21-24 (2001); Trends in Logic, ...

Author: Benedikt Löwe

Publisher: Springer

ISBN: 364221875X

Category: Computers

Page: 319

View: 570

This book constitutes the refereed proceedings of the 7th Conference on Computability in Europe, CiE 2011, held in Sofia, Bulgaria, in June/July 2011. The 22 revised papers presented together with 11 invited lectures were carefully reviewed and selected with an acceptance rate of under 40%. The papers cover the topics computability in analysis, algebra, and geometry; classical computability theory; natural computing; relations between the physical world and formal models of computability; theory of transfinite computations; and computational linguistics.

Machines Computations and Universality

Classical and New Paradigms of Computation and their Complexity Hierarchies. Trends in Logic, vol. 23, pp. 141–158. Kluwer Academic Publishers, Dordrecht (2004) [Ham05] Hamkins, J.D.: Infinitary computability with infinite time Turing ...

Author: Jérôme Durand-Lose

Publisher: Springer Science & Business Media

ISBN: 3540745920

Category: Computers

Page: 324

View: 563

This book constitutes the refereed proceedings of the 5th International Conference on Machines, Computations, and Universality, MCU 2007, held in Orleans, France, September 10-13, 2007. The 18 revised full papers presented together with 9 invited papers were carefully reviewed and selected. The topics include Turing machines, register machines, word processing, cellular automata, tiling of the plane, neural networks, molecular computations, BSS machines, infinite cellular automata, real machines, and quantum computing.

Effective Mathematics of the Uncountable

(special issue devoted to hypercomputation). [6] Joel David Hamkins. Supertask computation. In Boris Piwinger Benedikt L ̈owe and Thoralf R ̈asch, editors, Classical and New Paradigms of Computation and their Complexity Hierarchies, ...

Author: Noam Greenberg

Publisher: Cambridge University Press

ISBN: 1107014514

Category: Mathematics

Page: 204

View: 944

A comprehensive introduction to eight major approaches to computation on uncountable mathematical domains.