03474nam 22006615 450 991029919800332120220516172555.03-319-21750-X10.1007/978-3-319-21750-5(CKB)3710000000452174(EBL)3567907(SSID)ssj0001534639(PQKBManifestationID)11875888(PQKBTitleCode)TC0001534639(PQKBWorkID)11496484(PQKB)11566367(DE-He213)978-3-319-21750-5(MiAaPQ)EBC3567907(PPN)187686459(EXLCZ)99371000000045217420150724d2015 u| 0engur|n|---|||||txtccrComputational complexity of solving equation systems /by Przemysław Broniek1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (70 p.)SpringerBriefs in Philosophy,2211-4548Description based upon print version of record.3-319-21749-6 Includes bibliographical references.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.SpringerBriefs in Philosophy,2211-4548AlgorithmsLogicLogic, Symbolic and mathematicalAlgorithm Analysis and Problem Complexityhttps://scigraph.springernature.com/ontologies/product-market-codes/I16021Logichttps://scigraph.springernature.com/ontologies/product-market-codes/E16000Mathematical Logic and Foundationshttps://scigraph.springernature.com/ontologies/product-market-codes/M24005Algorithms.Logic.Logic, Symbolic and mathematical.Algorithm Analysis and Problem Complexity.Logic.Mathematical Logic and Foundations.512.94Broniek Przemysławauthttp://id.loc.gov/vocabulary/relators/aut1060010MiAaPQMiAaPQMiAaPQBOOK9910299198003321Computational Complexity of Solving Equation Systems2510143UNINA