On some promise classes in structural complexity theory

To my parents iv Acknowledgments Professor Gerd Wechsung, my advisor, has been the most influential and decisive person regarding my scientific career. He not only nurtured my pleasure in mathematics when I was an undergraduate student but also introduced me to the joy and challenge of doing research. I very much appreciate his inspiring and enthusiastic way of creating and formalizing ideas and his graceful style of holding lectures as well as his humane warmth, grace, and optimism. I am particularly grateful to him for bringing about my collaboration with Professor Lane Hemaspaandra and, in general, for his constant encouragement and support. I am very grateful to Professor Lane Hemaspaandra for his kind guidance, insightful advice, and seminal collaboration during my one year stay at the University of Rochester and ever since. His scientific enthusiasm and his flood of wonderful ideas, comments, and suggestions that contributed to the research described in this work have been invaluable for this thesis and, in fact, made it possible at all. Particularly, I am much indebted to him for having me take part in, and contribute to, his research projects, which eventually led to the first three sections of Chapter 3 and to Chapter 5 of this thesis. From him I learned that striking out in new directions from the solid foundation of being well versed in one's field, combined with the American virtue, speed in getting done whatever one aims at, is the most crucial prerequisite for successful work. In addition, I thank him for his financial support that allowed me to present the results contained in the fourth section of Chapter 3 at the Acknowledgments Jena for our wonderful collaboration in many projects and for their generous permission to present the results of our joint papers in this thesis. In particular, I'd like to mention that Osamu Watanabe's idea of looking at Buhrman, E. Hemaspaandra, and Longpré's tally encoding of sparse sets ignited the research described in Chapter 4 of this thesis, and I again have to thank Lane Hemaspaandra for proposing the investigation of the upward separation technique regarding promise classes. I also thank Arfst Nickelsen and Johannes Köbler for their permission to state and cite still unpublished results of theirs in this work. Furthermore, I thank all my current and former colleagues, Gerhard Lischke, Jörg Vogel (who was supervising my diploma thesis in 1991), In particular, I'd like to express …