A Graphic Apology for Symmetry and Implicitness

Erscheinungsjahr 2000
ISBN: 978-0-19-850729-1
Verlag: OUP Oxford

Buch, Englisch, 520 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 945 g

The present book brings into focus the contrast between explicit and implicit algorithmic descriptions of objects. 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).

Autoren/Hrsg.

Carbone, Alessandra

Semmes, Stephen

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Wissenschaften: Theorie, Epistemologie, Methodik
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Geisteswissenschaften Philosophie Geschichte der Westlichen Philosophie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie

Inhaltsverzeichnis

- 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

Über Autor(innen)

A. Carbone, Associate Professor of Computer Science, University of Paris XII, France S. Semmes, Professor of Mathematics, Rice University, Houston, USA