Parameterized Complexity in 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 science-in particular methods from (parameterized) complexity theory-to problems in computational logic, artificial intelligence (AI), and knowledge representation & reasoning (KRR). He wrote his PhD thesis-titled Parameterized Complexity in the Polynomial Hierarchy-at 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.

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.