This book contains selected results of my PhD studies, carried out according to an individual binational agreement between TU Wien (Austria) and the university of Potsdam (Germany), from 2015 to 2021. Originally, it appeared as my PhD thesis, for which I was awarded with the EurAI Dissertation Award 2021 (See: https://www.eurai.org/award/markus-hecher). As a result, this book is published in the series Frontiers in Artificial Intelligence and Applications – Dissertations in Artificial Intelligence (FAIA-DAIS) by IOS Press; see [Hecher, 2022] for an extended abstract.
The overall goal of this book is to present a new toolkit on using the structural parameter treewidth for problems in knowledge representation and reasoning (KR) and artificial intelligence (AI), thereby establishing both theoretical upper and lower bounds, as well as methods to efficiently deal with treewidth in practice. Key foundations of this work provide runtime lower bounds for evaluating Quantified Boolean formulas (and logic programs), which — under reasonable assumptions in computational complexity — match known upper bounds that were published back in 2004 (and 2009). By the general nature of the developed tools and techniques, we expect a wide applicability beyond the selected problems and formalisms tackled in this book. We hope that this book will serve as a starting point in establishing further results and gaining deeper insights that foster future theoretical and practical investigations. For current follow-up works and up-to-date research, I refer to my website at TU Wien (See: https://dbai.tuwien.ac.at/staff/hecher).
I am very grateful for everybody, who supported this work. More detailed acknowledgements are below.