Computational Complexity of Solving Equation Systems

Przemysław Broniek (Autor)

Buch | Softcover

IX, 64 Seiten

2015 | 1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-21749-9 (ISBN)

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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.

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.

Erscheint lt. Verlag	5.8.2015
Reihe/Serie	SpringerBriefs in Philosophy
Zusatzinfo	IX, 64 p. 1 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Geisteswissenschaften ► Philosophie ► Logik
	Informatik ► Theorie / Studium ► Algorithmen
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Algorithm analysis and problem complexity • four-element 2-valued algebras • generic operations with few values • open problems • reducing CSP to SYSTERMSAT over unary algebras • simplification algorithm • three-element algebras • Unary algebras • width and complexity of unary algebras
ISBN-10	3-319-21749-6 / 3319217496
ISBN-13	978-3-319-21749-9 / 9783319217499
Zustand	Neuware