Computational Complexity of Solving Equation Systems

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.

Table des matières

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.

Résumé

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.

Détails du produit

• Auteurs: Przemys¿aw Broniek, Przemyslaw Broniek, Przemysław Broniek
• Edition: Springer, Berlin
• Langues: Anglais
• Format d'édition: Livre de poche
• Sortie: 01.01.2015
• EAN: 9783319217499
• ISBN: 978-3-31-921749-9
• Pages: 64
• Dimensions: 156 mm x 236 mm x 7 mm
• Poids: 131 g
• Illustrations: IX, 64 p. 1 illus.
• Thèmes: SpringerBriefs in Philosophy; SpringerBriefs in Philosophy
• Catégories: Sciences humaines, art, musique > Philosophie; Sciences naturelles, médecine, informatique, technique > Mathématiques > Théorie des probabilités, stochastique, statistiques; C, Algorithms, Logic, mathematische Grundlagen, Mathematik: Logik, computer science, Theory of Computation, Philosophie: Logik, Algorithm Analysis and Problem Complexity, Mathematical logic, Mathematical Logic and Foundations, Mathematical foundations, Philosophy: logic