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