Description
The book "A Graphic Apology for Symmetry and Implicitness" explores the difference between explicit and implicit algorithms and introduces a new geometric language for studying complexity theory. It covers a range of topics including graphs, formal proofs, languages, automata, groups, circuits, and complexity classes. The focus is on moderate complexity, but objects with higher complexity are also discussed. The book also delves into connections with geometry and metric spaces.
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).
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