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Computational complexity of solving ...

Broniek, Przemyslaw.

Computational complexity of solving equation systems[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	511.352
書名/作者:	Computational complexity of solving equation systems/ by Przemyslaw Broniek.
作者:	Broniek, Przemyslaw.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	ix, 64 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Computational complexity.
標題:	Equations - Numerical solutions.
標題:	Computer Science.
標題:	Algorithm Analysis and Problem Complexity.
標題:	Logic.
標題:	Mathematical Logic and Foundations.
ISBN:	9783319217505 (electronic bk.)
ISBN:	9783319217499 (paper)
內容註:	Acknowledgments -- Chapter 1. Introduction -- Chapter 2. Unary algebras -- Chapter 3. Reducing CSP to SYSTERMSAT over unary algebras -- Chapter 4. Partial characterizations -- Chapter 5. Conclusions and Open Problems.
摘要、提要註:	This volume considers the computational complexity of determining whether a system of equations over a fixed algebra A has a solution. It examines in detail the two problems this leads to: SysTermSat(A) and SysPolSat(A), in which equations are built out of terms or polynomials, respectively. The book characterizes those algebras for which SysPolSat can be solved in a polynomial time. So far, studies and their outcomes have not covered algebras that generate a variety admitting type 1 in the sense of Tame Congruence Theory. Since unary algebras admit only type 1, this book focuses on these algebras to tackle the main problem. It discusses several aspects of unary algebras and proves that the Constraint Satisfaction Problem for relational structures is polynomially equivalent to SysTermSat over unary algebras. The book's final chapters discuss partial characterizations, present conclusions, and describe the problems that are still open.
電子資源:	http://dx.doi.org/10.1007/978-3-319-21750-5

Computational complexity of solving equation systems[electronic resource] /
Broniek, Przemyslaw.

Computational complexity of solving equation systems[electronic resource] /by Przemyslaw Broniek. - Cham :Springer International Publishing :2015. - ix, 64 p. :ill., digital ;24 cm. - SpringerBriefs in philosophy,2211-4548. - SpringerBriefs in philosophy..

Acknowledgments -- Chapter 1. Introduction -- Chapter 2. Unary algebras -- Chapter 3. Reducing CSP to SYSTERMSAT over unary algebras -- Chapter 4. Partial characterizations -- Chapter 5. Conclusions and Open Problems.

This volume considers the computational complexity of determining whether a system of equations over a fixed algebra A has a solution. It examines in detail the two problems this leads to: SysTermSat(A) and SysPolSat(A), in which equations are built out of terms or polynomials, respectively. The book characterizes those algebras for which SysPolSat can be solved in a polynomial time. So far, studies and their outcomes have not covered algebras that generate a variety admitting type 1 in the sense of Tame Congruence Theory. Since unary algebras admit only type 1, this book focuses on these algebras to tackle the main problem. It discusses several aspects of unary algebras and proves that the Constraint Satisfaction Problem for relational structures is polynomially equivalent to SysTermSat over unary algebras. The book's final chapters discuss partial characterizations, present conclusions, and describe the problems that are still open.

ISBN: 9783319217505 (electronic bk.)

Standard No.: 10.1007/978-3-319-21750-5doiSubjects--Topical Terms:

393856
Computational complexity.

LC Class. No.: QA267.7

Dewey Class. No.: 511.352

Computational complexity of solving equation systems[electronic resource] /
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245 1 0 $a Computational complexity of solving equation systems $h [electronic resource] / $c by Przemyslaw Broniek.
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490 1 $a SpringerBriefs in philosophy, $x 2211-4548
505 0 $a Acknowledgments -- Chapter 1. Introduction -- Chapter 2. Unary algebras -- Chapter 3. Reducing CSP to SYSTERMSAT over unary algebras -- Chapter 4. Partial characterizations -- Chapter 5. Conclusions and Open Problems.
520 $a This volume considers the computational complexity of determining whether a system of equations over a fixed algebra A has a solution. It examines in detail the two problems this leads to: SysTermSat(A) and SysPolSat(A), in which equations are built out of terms or polynomials, respectively. The book characterizes those algebras for which SysPolSat can be solved in a polynomial time. So far, studies and their outcomes have not covered algebras that generate a variety admitting type 1 in the sense of Tame Congruence Theory. Since unary algebras admit only type 1, this book focuses on these algebras to tackle the main problem. It discusses several aspects of unary algebras and proves that the Constraint Satisfaction Problem for relational structures is polynomially equivalent to SysTermSat over unary algebras. The book's final chapters discuss partial characterizations, present conclusions, and describe the problems that are still open.
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650 0 $a Equations $x Numerical solutions. $3 492834
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650 2 4 $a Algorithm Analysis and Problem Complexity. $3 463701
650 2 4 $a Logic. $3 191646
650 2 4 $a Mathematical Logic and Foundations. $3 464911
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