Computational complexity of solving equation systems [electronic resource] / Przemysław Broniek.
2015
QA267.7
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Title
Computational complexity of solving equation systems [electronic resource] / Przemysław Broniek.
Author
Broniek, Przemysław, author.
ISBN
9783319217505 electronic book
331921750X electronic book
9783319217499
331921750X electronic book
9783319217499
Published
Cham : Springer, 2015.
Language
English
Description
1 online resource (ix, 64 pages) : illustration.
Call Number
QA267.7
Dewey Decimal Classification
511.3/52
Summary
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.
Bibliography, etc. Note
Includes bibliographical references.
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Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 29, 2015).
Series
SpringerBriefs in philosophy.
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Table of Contents
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.
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.