Computational Complexity of Solving Equation Systems

1. Auflage 2015
ISBN: 978-3-319-21749-9
Verlag: Springer International Publishing

Buch, Englisch, 64 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 1299 g

Reihe: SpringerBriefs in Philosophy

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.

Zielgruppe

Research

Autoren/Hrsg.

Broniek, Przemys¿aw

Broniek, Przemyslaw

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Computeralgebra
• Mathematik | Informatik EDV | Informatik Informatik Berechenbarkeitstheorie, Komplexitätstheorie

Inhaltsverzeichnis

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.