Bounded Queries in Recursion Theory

One of the major concerns of theoretical computer science is the classifi cation of problems in terms of how hard they are.

Author: William Levine

Publisher: Springer Science & Business Media

ISBN: 9781461206354

Category: Computers

Page: 353

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One of the major concerns of theoretical computer science is the classifi cation of problems in terms of how hard they are. The natural measure of difficulty of a function is the amount of time needed to compute it (as a function of the length of the input). Other resources, such as space, have also been considered. In recursion theory, by contrast, a function is considered to be easy to compute if there exists some algorithm that computes it. We wish to classify functions that are hard, i.e., not computable, in a quantitative way. We cannot use time or space, since the functions are not even computable. We cannot use Turing degree, since this notion is not quantitative. Hence we need a new notion of complexity-much like time or spac~that is quantitative and yet in some way captures the level of difficulty (such as the Turing degree) of a function.
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Models and Computability

Bounded queries in recursion theory: A survey. Proceedings of the sirrth Annual Conference on Structure in Complexity Theory, IEEE Computer Society Press, 62-78, 1991. [28] W. Gasarch. A hierarchy of functions with applications to ...

Author: England) Logic Colloquium '97 (1997: Leeds

Publisher: Cambridge University Press

ISBN: 9780521635509

Category: Mathematics

Page: 419

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Second of two volumes providing a comprehensive guide to the current state of mathematical logic.
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Mathematical Foundations of Computer Science 1996

It is for these reasons that the theory of bounded queries in recursion theory was developed ( 1 , 2 , 6 ] . Given that a function f is recursive in a set X , our main concern will be the number of queries to X required to compute f .

Author: Symposium on Mathematical Foundations of Computer Science (1972- ) 199

Publisher: Springer Science & Business Media

ISBN: 3540615504

Category: Computers

Page: 592

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This book constitutes the refereed proceedings of the 21st International Symposium on Mathematical Foundations of Computer Science, MFCS '96, held in Crakow, Poland in September 1996. The volume presents 35 revised full papers selected from a total of 95 submissions together with 8 invited papers and 2 abstracts of invited talks. The papers included cover issues from the whole area of theoretical computer science, with a certain emphasis on mathematical and logical foundations. The 10 invited presentations are of particular value.
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Complexity Logic and Recursion Theory

Decidable theories ( Theorem 6.14 ) . 11. More recursion theory than you want to know ( the table in Section 7.1 ) . 12. Bounded queries ( Theorem 7.17.6 ) . We again state what we consider to be the most important open problem in the ...

Author: Andrea Sorbi

Publisher: CRC Press

ISBN: 0824700260

Category: Mathematics

Page: 384

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"Integrates two classical approaches to computability. Offers detailed coverage of recent research at the interface of logic, computability theory, nd theoretical computer science. Presents new, never-before-published results and provides informtion not easily accessible in the literature."
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FSTTCS 2004 Foundations of Software Technology and Theoretical Computer Science

Bounded Queries in Recursion Theory. Birkhauser, 1998. [Gol67] E. M. Gold. Language identification in the limit. Information and Control, 10:447–474, 1967. [IJ88] O. Ibarra and T. Jiang. Learning regular languages from counterexamples.

Author: Kamal Lodaya

Publisher: Springer Science & Business Media

ISBN: 9783540240587

Category: Computers

Page: 532

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This book constitutes the refereed proceedings of the 24th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2004, held in Chennai, India, in December 2004. The 35 revised full papers presented together with 5 invited papers were carefully reviewed and selected from 176 submissions. The papers address a broad variety of current issues in software science, programming theory, systems design and analysis, formal methods, mathematical logic, mathematical foundations, discrete mathematics, combinatorial mathematics, complexity theory, automata theory, and theoretical computer science in general.
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Computability and Models

A hierarchy of functions with applications to recursive graph theory . Technical Report 1651 , University of Maryland , Dept. of Computer Science . Gasarch , William and Martin , Georgia ( 1999 ) . Bounded Queries in Recursion Theory .

Author: Barry S. Cooper

Publisher: Springer Science & Business Media

ISBN: 030647400X

Category: Computers

Page: 375

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There are few notions as fundamental to contemporary science as those of computability and modelling. Computability and Models attempts to make some of the exciting and important new research developments in this area accessible to a wider readership. Written by international leaders drawn from major research centres both East and West, this book is an essential addition to scientific libraries serving both specialist and the interested non-specialist reader.
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Mathematical Foundations of Computer Science 2004

Bounded queries in recursion theory: A survey. In Proc. 6th Structure in Complexity Theory, 1991. L. Hemaspaandra, A. Hoene, and M. Ogihara. Reducibility classes of p-selective sets. Theoretical Computer Science, 155:447–457, 1996.

Author: Jirí Fiala

Publisher: Springer

ISBN: 9783540286295

Category: Computers

Page: 904

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This volume contains the papers presented at the 29th Symposium on Mat- matical Foundations of Computer Science, MFCS 2004, held in Prague, Czech Republic, August 22–27, 2004. The conference was organized by the Institute for Theoretical Computer Science (ITI) and the Department of Theoretical Com- terScienceandMathematicalLogic(KTIML)oftheFacultyofMathematicsand Physics of Charles University in Prague. It was supported in part by the Eu- pean Association for Theoretical Computer Science (EATCS) and the European Research Consortium for Informatics and Mathematics (ERCIM). Traditionally, the MFCS symposia encourage high-quality research in all branches of theoretical computer science. Ranging in scope from automata, f- mal languages, data structures, algorithms and computational geometry to c- plexitytheory,modelsofcomputation,andapplicationsincludingcomputational biology, cryptography, security and arti?cial intelligence, the conference o?ers a unique opportunity to researchers from diverse areas to meet and present their results to a general audience. The scienti?c program of this year’s MFCS took place in the lecture halls of the recently reconstructed building of the Faculty of Mathematics and P- sics in the historical center of Prague, with the famous Prague Castle and other celebratedhistoricalmonumentsinsight.Theviewfromthewindowswasach- lengingcompetitionforthespeakersinthe?ghtfortheattentionoftheaudience. But we did not fear the result: Due to the unusually tough competition for this year’s MFCS, the admitted presentations certainly attracted considerable in- rest. The conference program (and the proceedings) consisted of 60 contributed papers selected by the Program Committee from a total of 167 submissions.
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Learning Theory

Theoretical Computer Science, 25:193–220, 1983. [GM98] W. Gasarch and G. Martin. Bounded Queries in Recursion Theory. Birkhauser, 1998. [Gol67] E. M. Gold. Language identification in the limit. Information and Control, 10:447–474, 1967.

Author: Gábor Lugosi

Publisher: Springer Science & Business Media

ISBN: 9783540352945

Category: Computers

Page: 656

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This book constitutes the refereed proceedings of the 19th Annual Conference on Learning Theory, COLT 2006, held in Pittsburgh, Pennsylvania, USA in June 2006. The 43 revised full papers presented together with 2 articles on open problems and 3 invited lectures were carefully reviewed and selected from a total of 102 submissions. The papers cover a wide range of topics including clustering, un- and semisupervised learning, statistical learning theory, regularized learning and kernel methods, query learning and teaching, inductive inference, learning algorithms and limitations on learning, online aggregation, online prediction and reinforcement learning.
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STACS 93

10th Annual Symposium on Theoretical Aspects of Computer Science, Würzburg, Germany, February 25-27, 1993. ... Bounded queries to SAT and the boolean hierachy . Theoretical Computer ... Bounded queries in recursion theory : A survey .

Author: Patrice Enjalbert

Publisher: Springer Science & Business Media

ISBN: 3540565035

Category: Computers

Page: 723

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This volume contains the proceedings of the tenth annual Symposium on Theoretical Aspects of Computer Science (STACS '93), held in W}rzburg, February 25-27, 1993. The STACS symposia are held alternately in Germany and France, and organized jointly by the Special Interest Group for Theoretical Computer Science of the Gesellschaft f}r Informatik (GI) and theSpecial Interest Group for Applied Mathematics of the Association Francaise des Sciences et Technologies de l'Information et des Syst mes (afcet). The volume includes the three invited talks which opened the three days of the symposium: "Causal and distributed semantics for concurrent processes" (I. Castellani), "Parallel architectures: design and efficient use" (B. Monien et al.), and "Transparent proofs" (L. Babai). The selection of contributed papers is organized into parts on: computational complexity, logic in computer science, efficient algorithms, parallel and distributed computation, language theory, computational geometry, automata theory, semantics and logic of programming languages, automata theory and logic, circuit complexity, omega-automata, non-classical complexity, learning theory and cryptography, and systems.
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Mathematical Foundations of Computer Science 1995

Bounded queries in recursion theory : a survey . In Proceedings of the Sixth Annual Structure in Complexity Theory Conference . IEEE Computer Society Press , 62–78 , 1991 . 6. V. Harizanov , M. Kummer , J. C. Owings , Jr. Frequency ...

Author: International Symposium on Mathematical Foundations of Computer Science (20 : 1995 : Praha)

Publisher: Springer Science & Business Media

ISBN: 3540602461

Category: Computers

Page: 588

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This book presents the proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science, MFCS'95, held in Prague, Czech Republic in August/September 1995. The book contains eight invited papers and two abstracts of invited talks by outstanding scientists as well as 44 revised full research papers selected from a total of 104 submissions. All relevant aspects of theoretical computer science are addressed, particularly the mathematical foundations; the papers are organized in sections on structural complexity, algorithms, complexity theory, graphs in models of computation, lower bounds, formal languages, unification, rewriting and type theory, distributed computation, concurrency, semantics, model checking, and formal calculi.
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Algorithmic Learning Theory

Bounded Queries in Recursion Theory. Birkhauser, 1998. E. M. Gold. Language identification in the limit. Information and Control, 10:447–474, 1967. W. Gasarch and M. Pleszkoch. Learning via queries to an oracle.

Author: Shai Ben David

Publisher: Springer

ISBN: 9783540302155

Category: Computers

Page: 514

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Algorithmic learning theory is mathematics about computer programs which learn from experience. This involves considerable interaction between various mathematical disciplines including theory of computation, statistics, and c- binatorics. There is also considerable interaction with the practical, empirical ?elds of machine and statistical learning in which a principal aim is to predict, from past data about phenomena, useful features of future data from the same phenomena. The papers in this volume cover a broad range of topics of current research in the ?eld of algorithmic learning theory. We have divided the 29 technical, contributed papers in this volume into eight categories (corresponding to eight sessions) re?ecting this broad range. The categories featured are Inductive Inf- ence, Approximate Optimization Algorithms, Online Sequence Prediction, S- tistical Analysis of Unlabeled Data, PAC Learning & Boosting, Statistical - pervisedLearning,LogicBasedLearning,andQuery&ReinforcementLearning. Below we give a brief overview of the ?eld, placing each of these topics in the general context of the ?eld. Formal models of automated learning re?ect various facets of the wide range of activities that can be viewed as learning. A ?rst dichotomy is between viewing learning as an inde?nite process and viewing it as a ?nite activity with a de?ned termination. Inductive Inference models focus on inde?nite learning processes, requiring only eventual success of the learner to converge to a satisfactory conclusion.
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Fundamentals of Computation Theory

Bounded queries in recursion theory: A survey. In Proceedings of the Sixth Annual Structure in Complexity Theory Conference, pages 62–78. IEEE Computer Soc. Press, 1991. 8. V. Harizanov, M. Kummer, and J. Owings.

Author: Andrzej Lingas

Publisher: Springer

ISBN: 9783540450771

Category: Computers

Page: 440

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This book constitutes the refereed proceedings of the 14th International Symposium Fundamentals of Computation Theory, FCT 2003, held in Malmö, Sweden in August 2003. The 36 revised full papers presented together with an invited paper and the abstracts of 2 invited talks were carefully reviewed and selected from 73 submissions. The papers are organized in topical sections on approximibility, algorithms, networks and complexity, computational biology, computational geometry, computational models and complexity, structural complexity, formal languages, and logic.
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Mathematical Foundations of Computer Science 2002

finite tree cannot be embedded into it, then all its branches are recursive. It is not clear what the correct transferal of this lemma to ... Computation, 82(1):34–44, 1989. 6. W. Gasarch. Bounded queries in recursion theory: A survey.

Author: Krzystof Diks

Publisher: Springer

ISBN: 9783540456872

Category: Computers

Page: 660

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This book constitutes the refereed proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science, MFCS 2002, held in Warsaw, Poland in August 2002. The 48 revised full papers presented together with 5 invited papers were carefully reviewed and selected from 108 submissions. All relevant aspects of theoretical computer science are addressed, ranging from discrete mathematics, combinatorial optimization, graph theory, algorithms, and complexity to programming theory, formal methods, and mathematical logic.
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STACS 2002

Bounded Queries in Recursion Theory. Birkhäuser, 1999. 10. C. G. Jockusch, Jr. Reducibilities in Recursive Function Theory. PhD thesis, MIT, Cambridge, Massachusetts, 1966. 11. E. B. Kinber. Frequency computations in finite automata.

Author: Helmut Alt

Publisher: Springer

ISBN: 9783540458418

Category: Computers

Page: 660

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This book constitutes the refereed proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2002, held in Antibes - Juan les Pins, France, in March 2002. The 50 revised full papers presented together with three invited papers were carefully reviewed and selected from a total of 209 submissions. The book offers topical sections on algorithms, current challenges, computational and structural complexity, automata and formal languages, and logic in computer science.
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Mathematical Foundations of Computer Science 2005

Bounded queries in recursion theory: A survey. In Proc. 6th Structure in Complexity Theory, 1991. J. Goldsmith, D. Joseph, and P. Young. ... Theoretical Computer Science, 155:447–457, 1996. L. Hemaspaandra, Z. Jiang, J. Rothe, ...

Author: Joanna Jedrzejowicz

Publisher: Springer

ISBN: 9783540318675

Category: Computers

Page: 814

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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.
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STACS 95

Bounded queries in recursion theory : a survey . In : Proceedings Structure in Complexity Theory . Sixth Annual Conference , pp.62-78 , IEEE Computer Society Press , 1991 . ( GN94 ] Xiaolin Ge , Anil Nerode . On extreme points of convex ...

Author: Ernst W. Mayr

Publisher: Springer Science & Business Media

ISBN: 3540590420

Category: Computers

Page: 654

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This book presents the proceedings of the 12th Annual Symposium on Theoretical Aspects of Computer Science (STACS 95), held in Munich, Germany in March 1995. Besides three invited talks, the book contains revised versions of 53 research papers selected from a total of 180 submissions. The contributions address all current aspects of theoretical computer science; they are organized in sections on complexity theory, automata theory, algorithms, logic, theory of parallel computing, communication theory, graph theory and databases, and computational geometry.
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Cryptographic Applications of Analytic Number Theory

Complexity Lower Bounds ( 1999 ) PCS 11 : Snyder , W. ( Ed . ) A Proof Theory for General Unification ( 1992 ) ISBN 0-8176-3593-9 PCS 16 : Gasarch , W. / Martin , G. Bounded Queries in Recursion Theory ( 1998 ) ISBN ...

Author: Igor Shparlinski

Publisher: Springer Science & Business Media

ISBN: 3764366540

Category: Computers

Page: 411

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The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Cryptographers and number theorists will find this book useful. The former can learn about new number theoretic techniques which have proved to be invaluable cryptographic tools, the latter about new challenging areas of applications of their skills.
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Automata Theory and its Applications

... Johannes Grabmeier, & Volker Weispfenning Bounded Queries in Recursion Theory William I. Gasarch & Georgia A. Martin Number Theoretic Methods in Cryptography: Complexity lower bounds I. Shparlinski Interpolating Cubic Splines Gary ...

Author: Bakhadyr Khoussainov

Publisher: Springer Science & Business Media

ISBN: 9781461201717

Category: Mathematics

Page: 432

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The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.
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Advances in Computers

He has written a book, with Georgia Martin, on “Bounded Queries in Recursion Theory.” He currently coblogs (with Lance Fortnow) complexity blog which is a well-read blog on complexity theory. CHAPTER FIVE Advances in Testing ...

Author:

Publisher: Academic Press

ISBN: 9780128023419

Category: Computers

Page: 276

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Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in computer hardware, software, theory, design, and applications. It has also provided contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. As a result, many articles have become standard references that continue to be of significant, lasting value in this rapidly expanding field. In-depth surveys and tutorials on new computer technology Well-known authors and researchers in the field Extensive bibliographies with most chapters Many of the volumes are devoted to single themes or subfields of computer science
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