Completeness and Reduction in Algebraic Complexity Theory

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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.