Boolean hierarchies - on collapse properties and query order

To my family Acknowledgements Words can not express my deep gratitude to my advisor Professor Gerd Wechsung. Generously he ooered support, guidance, and encouragement throughout the past four years. Learning from him and working with him was and still is a pleasure and privilege I much appreciate. Through all the ups and downs of my research his optimism and humane warmth have made the downs less frustrating and the ups more encouraging. I want to express my deep gratitude to Professor Lane Hemaspaandra and Professor Edith Hemaspaandra. Allowing me to becomepart of so many joint projects has beena wonderful learning experience and I much beneeted from their scientiic expertise. Their generous help and advice helped me to gain insights into how research is done and made this thesis possible. For serving as referees for this thesis I am grateful to Professor Edith Hemaspaandra and Professor Klaus Wagner. I w ant to thank all my colleagues at Jena, especially, Haiko M uller, Dieter Kratsch, JJ org Rothe, Johannes Waldmann, and Maren Hinrichs for generously ooering help and support regarding the many little things that scientiic work seems to require these days (L A T E X, unix, email, etc). Working in the theory group of Professor Gerd Wechsung has made the past years a wonderful time. I w ant to thank my p a r e n ts who brought about my i n terest into mathematics. For their encouragement and support I am grateful to my family, m y mother-in-law, and most of all, my l o ving wife Ines. Chapter 3 and Section 4.2 are based on joint w ork with Edith Hemaspaandra and Lane Hemaspaandra HHH98d] and part of it appeared in journal as HHH98e]. The research underlying Section 4.3 is joint work with Edith Hemaspaandra and Lane Hemaspaandra HHH98a]. The results of Section 5.2 were discovered jointly with Lane Hemaspaandra and Gerd Wechsung and will appear in journal as HHW99]. Section 5.4 is based on joint w ork with Edith Hemaspaandra and Lane Hemaspaandra and has (partially) appeared in journal as HHH97a].

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