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Computational Complexity of Solving Equation Systems [electronic resource] / by Przemys�aw Broniek.

By: Broniek, Przemys�aw [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: SpringerBriefs in Philosophy: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2015Edition: 1st ed. 2015.Description: IX, 64 p. 1 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319217505.Subject(s): Computer science | Logic | Algorithms | Mathematical logic | Computer Science | Algorithm Analysis and Problem Complexity | Logic | Mathematical Logic and FoundationsAdditional physical formats: Printed edition:: No titleDDC classification: 005.1 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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