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Computational Complexity of Solving Equation Systems: SpringerBriefs in Philosophy

Autor Przemysław Broniek
en Limba Engleză Paperback – 5 aug 2015
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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Specificații

ISBN-13: 9783319217499
ISBN-10: 3319217496
Pagini: 120
Ilustrații: IX, 64 p. 1 illus.
Dimensiuni: 155 x 235 x 7 mm
Greutate: 0.12 kg
Ediția:1st ed. 2015
Editura: Springer International Publishing
Colecția Springer
Seria SpringerBriefs in Philosophy

Locul publicării:Cham, Switzerland

Public țintă

Research

Cuprins

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.

Caracteristici

Introduces the reader to problems of solving systems of equations Describes and explains past solutions and provides definitions Reflects the state of the art in solving equation systems Includes supplementary material: sn.pub/extras