Computational Complexity of Solving Equation Systems / by Przemysław Broniek.

Format:

Book

Author/Creator:

Broniek, Przemysław, author.

Contributor:

SpringerLink (Online service)

Series:

Computer Science (Springer-11645)

SpringerBriefs in philosophy 2211-4548

SpringerBriefs in Philosophy, 2211-4548

Language:

English

Subjects (All):

Algorithms.

Logic.

Logic, Symbolic and mathematical.

Algorithm Analysis and Problem Complexity.

Mathematical Logic and Foundations.

Local Subjects:

Algorithm Analysis and Problem Complexity.

Logic.

Mathematical Logic and Foundations.

Physical Description:

1 online resource (IX, 64 pages) : 1 illustrations.

Edition:

First edition 2015.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

System Details:

text file PDF

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.

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.

Other Format:

Printed edition:

ISBN:

978-3-319-21750-5

9783319217505

Access Restriction:

Restricted for use by site license.