Overview
- 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
Part of the book series: SpringerBriefs in Philosophy (BRIEFSPHILOSOPH)
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Table of contents (5 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Computational Complexity of Solving Equation Systems
Authors: Przemysław Broniek
Series Title: SpringerBriefs in Philosophy
DOI: https://doi.org/10.1007/978-3-319-21750-5
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: The Author(s) 2015
Softcover ISBN: 978-3-319-21749-9Published: 05 August 2015
eBook ISBN: 978-3-319-21750-5Published: 24 July 2015
Series ISSN: 2211-4548
Series E-ISSN: 2211-4556
Edition Number: 1
Number of Pages: IX, 64
Number of Illustrations: 1 b/w illustrations
Topics: Algorithm Analysis and Problem Complexity, Logic, Mathematical Logic and Foundations