Parameterized Complexity in the Polynomial Hierarchy: Extending Parameterized Complexity Theory to Higher Levels of the Hierarchy

by Ronald de Haan

Overview

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.

Product Details

ISBN-13:	9783662606698
Publisher:	Springer Berlin Heidelberg
Publication date:	12/31/2019
Series:	Lecture Notes in Computer Science , #11880
Edition description:	1st ed. 2019
Pages:	398
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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.

Table of 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.