Algebraic Complexity Theory

Algebraic Complexity Theory

Algebraic Complexity Theory

Algebraic complexity theory investigates the computational cost of solving problems with an algebraic flavor. Several cost measures are of interest. We consider arithmetic circuits, which can perform the (exact) arithmetic operations +, -, *, / at unit cost, and take their size ( = sequential time) or their depth (=parallel time) as cost functions. This is a natural "structured" model of comput...

Independence in Algebraic Complexity Theory

Nicholas Pippenger Algebraic Complexity Theory

Algebraic complexity theory, the study of the minimum number of operations suficient o perform algebraic computations, is surveyed with emphasis on the general theory of bilinear forms and two of its applications: polynomial multiplication and matrix multiplication. Though by no means exhausting algebraic complexity theory, these topics illustrate well its development and its methods, and ...

Algebraic closures in complexity theory