Parameterized Complexity in the Polynomial Hierarchy was 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.
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.
Ronald de Haan is a postdoctoral researcher at the Institute for Logic, Language and Computation (ILLC) at the University of Amsterdam.His research interests include the application of methods from theoretical computer sciencein particular methods from (parameterized) complexity theoryto problems in computational logic, artificial intelligence (AI), and knowledge representation & reasoning (KRR).
He wrote his PhD thesistitled Parameterized Complexity in the Polynomial Hierarchyat the Algorithms and Complexity Group at the Faculty of Informatics of the Technische Universität Wien. He received his PhD in 2016. His PhD thesis was awarded the E.W. Beth Dissertation Prize 2017, was shortlisted for the Heinz Zemanek Prize 2018, and was nominated for the GI-Dissertationspreis 2016 of the German Informatics Society.
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