This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants.
1. Introduction.- 2. Valiant's Algebraic Model of NP-Completeness.- 3. Some Complete Families of Polynomials.- 4. Cook's versus Valiant's Hypothesis.- 5. The Structure of Valiant's Complexity Classes.- 6. Fast Evaluation of Representations of General Linear Groups.- 7. The Complexity of Immanants.- 8. Separation Results and Future Directions.- References.- List of Notations.- Index
Algebra Bürgisser, a top expert on algebraic complexity theory, has written a monograph on current research in this field. This book gives new results in the theory of NP-completeness. It is written for mathematicians and computer scientists on both rese
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