On the Extraction of Computational Content from Noneffective Convergence Proofs in Analysis PDF Download

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Publisher:
ISBN: 9783832591601
Category :
Languages : en
Pages :

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Author: Pavol Safarik
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832537651
Category : Computers
Languages : en
Pages : 164

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The Fields medalist, Terence Tao, recently emphasized the importance of ''hard'' (or finitary) analysis and connected the finitisation to the methods we will employ in this thesis: ... The main advantage of working in a finitary setting ... is that the underlying dynamical system becomes extremely explicit. ... In proof theory, this finitisation is known as Gödel functional interpretation ... For convergence theorems Tao calls the finitary formulation metastability and the corresponding explicit content its rate(s). In the case of the mean ergodic theorem such a rate can be used to obtain even an effective bound on the number of fluctuations. We introduce effective learnability and three other natural kinds of such finitary information and analyze the corresponding proof-theoretic conditions. Effective learnability not only provides means to know when to expect a bound on the number of fluctuations but also explains a very common pattern in the realizers for strong ergodic theorems. Moreover, we will see how a most natural example for a non-learnable convergence theorem closely relates to a notable exception to this pattern, the strong nonlinear ergodic theorem due to Wittmann. Finally, we show how can computational content be extracted in the context of non-standard analysis.

Author: Sergei Artemov
Publisher: Springer
ISBN: 3319720562
Category : Mathematics
Languages : en
Pages : 378

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This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2018, held in Deerfield Beach, FL, USA, in January 2018. The 22 revised full papers were carefully reviewed and selected from 22 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda andcombinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; and other logics in computer science.

Author: David F. Rosenthal
Publisher: CRC Press
ISBN: 1000149323
Category : Technology & Engineering
Languages : en
Pages : 417

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The interest of AI in problems related to understanding sounds has a rich history dating back to the ARPA Speech Understanding Project in the 1970s. While a great deal has been learned from this and subsequent speech understanding research, the goal of building systems that can understand general acoustic signals--continuous speech and/or non-speech sounds--from unconstrained environments is still unrealized. Instead, there are now systems that understand "clean" speech well in relatively noiseless laboratory environments, but that break down in more realistic, noisier environments. As seen in the "cocktail-party effect," humans and other mammals have the ability to selectively attend to sound from a particular source, even when it is mixed with other sounds. Computers also need to be able to decide which parts of a mixed acoustic signal are relevant to a particular purpose--which part should be interpreted as speech, and which should be interpreted as a door closing, an air conditioner humming, or another person interrupting. Observations such as these have led a number of researchers to conclude that research on speech understanding and on nonspeech understanding need to be united within a more general framework. Researchers have also begun trying to understand computational auditory frameworks as parts of larger perception systems whose purpose is to give a computer integrated information about the real world. Inspiration for this work ranges from research on how different sensors can be integrated to models of how humans' auditory apparatus works in concert with vision, proprioception, etc. Representing some of the most advanced work on computers understanding speech, this collection of papers covers the work being done to integrate speech and nonspeech understanding in computer systems.

Author:
Publisher:
ISBN:
Category : Algebraic Logic
Languages : en
Pages : 212

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Author: Sanjeev Arora
Publisher: Cambridge University Press
ISBN: 0521424267
Category : Computers
Languages : en
Pages : 609

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New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Author: Ulrich Kohlenbach
Publisher: Springer Science & Business Media
ISBN: 3540775331
Category : Mathematics
Languages : en
Pages : 539

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This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as – via extended case studies – carrying out some of these applications in full detail. This subject has historical roots in the 1950s. This book for the first time tells the whole story.

Author: Yousef Saad
Publisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292

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This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Author: Anol Bhattacherjee
Publisher: CreateSpace
ISBN: 9781475146127
Category : Science
Languages : en
Pages : 156

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This book is designed to introduce doctoral and graduate students to the process of conducting scientific research in the social sciences, business, education, public health, and related disciplines. It is a one-stop, comprehensive, and compact source for foundational concepts in behavioral research, and can serve as a stand-alone text or as a supplement to research readings in any doctoral seminar or research methods class. This book is currently used as a research text at universities on six continents and will shortly be available in nine different languages.

Author: Yousef Saad
Publisher: SIAM
ISBN: 0898715342
Category : Mathematics
Languages : en
Pages : 537

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Mathematics of Computing -- General.