ComputingComputer ScienceMathematicsAlgebraAlgorithmsTheory Of ComputationComplexity TheoryComputational ComplexityComputational ModelsRecursion TheoryLower BoundsPrecisionRecursive FunctionsTuring Machine ComputabilityTuring Machine Model
Publisher Summary This chapter discusses algebraic complexity theory. Complexity theory, as a project of lower bounds and optimality, unites two quite different traditions. The first comes from mathematical logic and the theory of recursive functions. In this, the basic computational model is the Turing machine. The second tradition has developed from questions of numerical algebra. The problems in this typically have a fixed finite size. Consequently, the computational model is based on something like an ordinary computer that however is supplied with the ability to perform any arithmetic operation with infinite precision and that in turn is required to deliver exact results. The formal model is that of straight-line program or arithmetic circuit or computation sequence, more generally that of computation tree.