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In a nice assay published in Nature in 1993 the physicist Richard God III started from a human observer and made a number of witty conclusions about our future prospects giving estimates for the existence of the Berlin Wall, the human race and all the rest of the universe. In the same spirit, we derive implications for "the meaning of life, the universe and all the rest" from few principles. Adams´ absurd answer "42" tells the lesson "garbage in / garbage out" - or suggests that the question is non calculable. We show that experience of "meaning" and to decide fundamental questions which can not be decided by formal systems imply central properties of life: Ever higher levels of internal representation of the world and an escalating tendency to become more complex. An observer, "collecting observations" and three measures for complexity are examined. A theory on living systems is derived focussing on their internal representation of information. Living systems are more complex than Kolmogorov complexity ("life is NOT simple") and overcome decision limits (Gödel theorem) for formal systems as illustrated for cell cycle. Only a world with very fine tuned environments allows life. Such a world is itself rather complex and hence excessive large in its space of different states – a living observer has thus a high probability to reside in a complex and fine tuned universe.

This thesis is devoted to the study of computational complexity theory, a branch of theoretical computer science. Computational complexity theory investigates the inherent difficulty in designing efficient algorithms for computational problems. By doing so, it analyses the scalability of computational problems and algorithms and places practical limits on what computers can actually accomplish. Computational problems are categorised into complexity classes. Among the most important complexity classes are the class NP and the subclass of NP-complete problems, which comprises many important optimisation problems in the field of operations research. Moreover, with the P-NP-problem, the class NP represents the most important unsolved question in computer science. The first part of this thesis is devoted to the study of NP-complete-, and more generally, NP-hard problems. It aims at improving our understanding of this important complexity class by systematically studying how altering NP-hard sets affects their NP-hardness. This research is related to longstanding open questions concerning the complexity of unions of disjoint NP-complete sets, and the existence of sparse NP-hard sets. The second part of the thesis is also dedicated to complexity classes but takes a different perspective: In a sense, after investigating the interior of complexity classes in the first part, the focus shifts to the description of complexity classes and thereby to the exterior in the second part. It deals with the description of complexity classes through leaf languages, a uniform framework which allows us to characterise a great variety of important complexity classes. The known concepts are complemented by a new leaf-language model. To a certain extent, this new approach combines the advantages of the known models. The presented results give evidence that the connection between the theory of formal languages and computational complexity theory might be closer than formerly known.