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).D 13.3 The visibility surjection problem Definition 13.5 Let G and K be oriented graphs without nontrivial oriented cycles, and let g : G a agt; K be a mapping between them. Fix a vertex v in g, and let g:V+(v, G)^V+(g(v), K) (13.11) be the inducedanbsp;...
|Title||:||A Graphic Apology for Symmetry and Implicitness|
|Author||:||Alessandra Carbone, Stephen Semmes|
|Publisher||:||OUP Oxford - 2000|