عنوان

Completeness and Reduction in Algebraic Complexity Theory

شابک

9783642086045

شابک

9783662041796

شماره

b407082

عنوان اصلي

Completeness and Reduction in Algebraic Complexity Theory

نام عام مواد

[Book]

نام نخستين پديدآور

by Peter Bürgisser.

محل نشرو پخش و غیره

Berlin, Heidelberg :

نام ناشر، پخش کننده و غيره

Imprint: Springer,

تاریخ نشرو بخش و غیره

2000.

عنوان فروست

Algorithms and Computation in Mathematics,

مشخصه جلد

7

شاپا ي ISSN فروست

1431-1550 ;

متن يادداشت

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 Notation.

بدون عنوان

0

متن يادداشت

One of the most important and successful theories in computational complex ity is that of NP-completeness. This discrete theory is based on the Turing machine model and achieves a classification of discrete computational prob lems according to their algorithmic difficulty. Turing machines formalize al gorithms which operate on finite strings of symbols over a finite alphabet. By contrast, in algebraic models of computation, the basic computational step is an arithmetic operation (or comparison) of elements of a fixed field, for in stance of real numbers. Hereby one assumes exact arithmetic. In 1989, Blum, Shub, and Smale [12] combined existing algebraic models of computation with the concept of uniformity and developed a theory of NP-completeness over the reals (BSS-model). Their paper created a renewed interest in the field of algebraic complexity and initiated new research directions. The ultimate goal of the BSS-model (and its future extensions) is to unite classical dis crete complexity theory with numerical analysis and thus to provide a deeper foundation of scientific computation (cf. [11, 101]). Already ten years before the BSS-paper, Valiant [107, 110] had proposed an analogue of the theory of NP-completeness in an entirely algebraic frame work, in connection with his famous hardness result for the permanent [108]. While the part of his theory based on the Turing approach (#P-completeness) is now standard and well-known among the theoretical computer science com munity, his algebraic completeness result for the permanents received much less attention.

شماره استاندارد بين المللي کتاب و موسيقي

9783642086045

عنوان

Springer eBooks

موضوع مستند نشده

Algebra.

موضوع مستند نشده

Computer science-- Mathematics.

موضوع مستند نشده

Information theory.

موضوع مستند نشده

Mathematics.

مستند نام اشخاص تاييد نشده

Bürgisser, Peter.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190301075800.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y