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A Graphic Apology for Symmetry and Implicitness

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Synopses & Reviews

Publisher Comments:

This book brings into focus the contrast between explicit and implicit algorithmic descriptions of objects and presents a new geometric language for the study of combinatorial and logical problems in complexity theory. These themes are considered in a variety of settings, sometimes crossing traditional boundaries. Special emphasis is given to moderate complexity - exponential or polynomial - but objects with multi-exponential complexity also fit in. Among the items under consideration are graphs, formal proofs, languages, automata, groups, circuits, some connections with geometry of metric spaces, and complexity classes (P, NP, co-NP).

Description:

Includes bibliographical references (p. [487]-495) and index.

Table of Contents

1. Introduction


2. Morphisms in logic and complexity


3. Exponential processes and formal proofs


4. Graphs and their visibilities


5. Asymptotic growth of infinite visibilities


6. Geometric aspects of cut elimination


7. Feasibility graphs


8. Bounds for finite visibilities


9. Some related computational questions


10. Mappings and graphs


11. Mappings and comparisons


12. Adjacency matrices and counting


13. Duality and NP-completeness


14. Finite automata and regular languages


15. Constructions with graphs


16. Stronger forms of recursion


17. Groups and graphs


18. Extended notions of automata


19. Geometry of scales in metric spaces


20. The Corona decomposition revisited


Appendix A: Formal proofs: A brief review


References


Index


Product Details

ISBN:
9780198507291
Author:
Carbone, Alessandra
Publisher:
Oxford University Press, USA
Author:
Semmes, Stephen
Author:
null, Alessandra
Author:
null, Stephen
Location:
Oxford
Subject:
Group Theory
Subject:
Mathematics | Pure Mathematics
Subject:
Machine Theory
Subject:
Computational complexity
Subject:
Logic
Subject:
Combinatorics
Subject:
Mathematics-Logic and Philosophy
Series:
Oxford mathematical monographs
Publication Date:
20000831
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
96 line illus
Pages:
520
Dimensions:
9 x 6.1 x 1.3 in 1.9 lb

Related Subjects

History and Social Science » Politics » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Combinatorics
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Group Theory
Science and Mathematics » Mathematics » Logic and Philosophy

A Graphic Apology for Symmetry and Implicitness New Hardcover
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Product details 520 pages Oxford University Press, USA - English 9780198507291 Reviews:
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