Gödel 96: Logical Foundations of Mathematics, Computer Science, and Physics de Petr Hajek

Gödel 96: Logical Foundations of Mathematics, Computer Science, and Physics: Lecture Notes in Logic 6

Petr Hajek

This volume contains the proceedings of the conference Logical Foundations of Mathematics, Computer Science, and Physics-Kurt Godel's Legacy, held in Brno, Czech Republic on the 90th anniversary of his birth. The wide and continuing importance of Godel s work in the logical foundations of mathematics, computer science, and physics is confirmed by the broad range of speakers who participated in making this gathering a scientific event.

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Cuprins

Preface -- Part I. Invited Papers -- Godel’s program for new axioms: Why, where, how and what? /@Solomon Feferman -- Infinite-valued Godel Logics with 0-1-Projections and Relativizations /@Matthias Baaz -- Contributions of K. Godel to Relativity and Cosmology /@G.F.E. Ellis -- Kurt Godel and the constructive Mathematics of A.A. Markov /@Boris A. Kushner -- Hao Wang as Philosopher /@Charles Parsons -- A bottom-up approach to foundations of mathematics /@Pavel Pudlak -- K-graph Machines: generalizing Turing’s machines and arguments /@Wilfried Sieg and John Byrnes -- Forcing on Bounded Arithmetic /@Gaisi Takeuti and Masahiro Yasumoto -- Uniform Interpolation and Layered Bisimulation -- A@@@lbert Visser -- Part II. Contributed Papers -- Godel’s Ontological Proof Revisited /@C. Anthony Anderson and Michael Gettings -- A Uniform Theorem Proving Tableau Method for Modal Logic /@Tadashi Araragi -- Decidability of the 3*V*-Class in the Membership Theory NWL /@Dorella Belle and Franco Parlamento -- A Logical Approach to Complexity Bounds for Subtype Inequalities /@Marcin Benke -- How to characterize provably total functions /@Benjamin Blankertz and Andreas Weiermann -- Completeness has to be restricted: Godel’s interpretation of the parameter t /@Giora Hon -- A Bounded Arithmetic Theory for Constant Depth Threshold Circuits /@Jan Johannsen -- Information content and computational complexity of recursive sets /@Lars Kristiansen -- Kurt Godel and the Consistency of R^^ /@Robert K. Meyer -- Best possible answer is computable for fuzzy SLD-resolution /@Leonard Pauh'k -- The finite stages of inductive definitions /@Robert F. Stark -- Godel and the Theory of Everything /@Michael Stoltzner -- Replacement- /-* Collection /@Andrzej M. Zarach

Descriere

Designed for introductory parallel computing courses at the advanced undergraduate or beginning graduate level, Elements of Parallel Computing presents the fundamental concepts of parallel computing not from the point of view of hardware, but from a more abstract view of algorithmic and implementation patterns. The aim is to facilitate the teaching of parallel programming by surveying some key algorithmic structures and programming models, together with an abstract representation of the underlying hardware. The presentation is friendly and informal. The content of the book is language neutral, using pseudocode that represents common programming language models.The first five chapters present core concepts in parallel computing. SIMD, shared memory, and distributed memory machine models are covered, along with a brief discussion of what their execution models look like. The book also discusses decomposition as a fundamental activity in parallel algorithmic design, starting with a naive example, and continuing with a discussion of some key algorithmic structures. Important programming models are presented in depth, as well as important concepts of performance analysis, including work-depth analysis of task graphs, communication analysis of distributed memory algorithms, key performance metrics, and a discussion of barriers to obtaining good performance. The second part of the book presents three case studies that reinforce the concepts of the earlier chapters. One feature of these chapters is to contrast different solutions to the same problem, using select problems that aren't discussed frequently in parallel computing textbooks. They include the Single Source Shortest Path Problem, the Eikonal equation, and a classical computational geometry problem: computation of the two-dimensional convex hull. After presenting the problem and sequential algorithms, each chapter first discusses the sources of parallelism then