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Parameterized Complexity in the Polynomial Hierarchy [electronic resource] : Extending Parameterized Complexity Theory to Higher Levels of the Hierarchy / by Ronald de Haan.

By: de Haan, Ronald [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Theoretical Computer Science and General Issues: 11880Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2019Edition: 1st ed. 2019.Description: XI, 398 p. 1349 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783662606704.Subject(s): Mathematical logic | Machine theory | Mathematical Logic and Foundations | Formal Languages and Automata TheoryAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 511.3 Online resources: Click here to access online
Contents:
Complexity Theory and Non-determinism -- Parameterized Complexity Theory -- Fpt-Reducibility to SAT -- The Need for a New Completeness Theory -- A New Completeness Theory -- Fpt-algorithms with Access to a SAT Oracle -- Problems in Knowledge Representation and Reasoning -- Model Checking for Temporal Logics -- Problems Related to Propositional Satisfiability -- Problems in Judgment Aggregation -- Planning Problems -- Graph Problems -- Relation to Other Topics in Complexity Theory -- Subexponential-Time Reductions -- Non-Uniform Parameterized Complexity -- Open Problems and Future Research Directions -- Conclusion -- Compendium of Parameterized Problems -- Generalization to Higher Levels of the Polynomial Hierarchy.
In: Springer Nature eBookSummary: The book presents the co-recipient of the E.W. Beth Dissertation Prize 2017 for outstanding dissertations in the fields of logic, language, and information. This work extends the theory of parameterized complexity to higher levels of the Polynomial Hierarchy (PH). For problems at higher levels of the PH, a promising solving approach is to develop fixed-parameter tractable reductions to SAT, and to subsequently use a SAT solving algorithm to solve the problem. In this dissertation, a theoretical toolbox is developed that can be used to classify in which cases this is possible. The use of this toolbox is illustrated by applying it to analyze a wide range of problems from various areas of computer science and artificial intelligence.
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Complexity Theory and Non-determinism -- Parameterized Complexity Theory -- Fpt-Reducibility to SAT -- The Need for a New Completeness Theory -- A New Completeness Theory -- Fpt-algorithms with Access to a SAT Oracle -- Problems in Knowledge Representation and Reasoning -- Model Checking for Temporal Logics -- Problems Related to Propositional Satisfiability -- Problems in Judgment Aggregation -- Planning Problems -- Graph Problems -- Relation to Other Topics in Complexity Theory -- Subexponential-Time Reductions -- Non-Uniform Parameterized Complexity -- Open Problems and Future Research Directions -- Conclusion -- Compendium of Parameterized Problems -- Generalization to Higher Levels of the Polynomial Hierarchy.

The book presents the co-recipient of the E.W. Beth Dissertation Prize 2017 for outstanding dissertations in the fields of logic, language, and information. This work extends the theory of parameterized complexity to higher levels of the Polynomial Hierarchy (PH). For problems at higher levels of the PH, a promising solving approach is to develop fixed-parameter tractable reductions to SAT, and to subsequently use a SAT solving algorithm to solve the problem. In this dissertation, a theoretical toolbox is developed that can be used to classify in which cases this is possible. The use of this toolbox is illustrated by applying it to analyze a wide range of problems from various areas of computer science and artificial intelligence.

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