@phdthesis{Reitwiessner2011,
  author    = {Reitwießner, Christian},
  title     = {Multiobjective Optimization and Language Equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-70146},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2011},
  abstract  = {Praktische Optimierungsprobleme beinhalten oft mehrere gleichberechtigte, sich jedoch widersprechende Kriterien. Beispielsweise will man bei einer Reise zugleich m{\"o}glichst schnell ankommen, sie soll aber auch nicht zu teuer sein. Im ersten Teil dieser Arbeit wird die algorithmische Beherrschbarkeit solcher mehrkriterieller Optimierungsprobleme behandelt. Es werden zun{\"a}chst verschiedene L{\"o}sungsbegriffe diskutiert und auf ihre Schwierigkeit hin verglichen. Interessanterweise stellt sich heraus, dass diese Begriffe f{\"u}r ein einkriterielles Problem stets gleich schwer sind, sie sich ab zwei Kriterien allerdings stark unterscheiden k{\"o}nen (außer es gilt P = NP). In diesem Zusammenhang wird auch die Beziehung zwischen Such- und Entscheidungsproblemen im Allgemeinen untersucht. Schließlich werden neue und verbesserte Approximationsalgorithmen f{\"u}r verschieden Varianten des Problems des Handlungsreisenden gefunden. Dabei wird mit Mitteln der Diskrepanztheorie eine Technik entwickelt, die ein grundlegendes Hindernis der Mehrkriteriellen Optimierung aus dem Weg schafft: Gegebene L{\"o}sungen so zu kombinieren, dass die neue L{\"o}sung in allen Kriterien m{\"o}glichst ausgewogen ist und gleichzeitig die Struktur der L{\"o}sungen nicht zu stark zerst{\"o}rt wird. Der zweite Teil der Arbeit widmet sich verschiedenen Aspekten von Gleichungssystemen f{\"u}r (formale) Sprachen. Einerseits werden konjunktive und Boolesche Grammatiken untersucht. Diese sind Erweiterungen der kontextfreien Grammatiken um explizite Durchschnitts- und Komplementoperationen. Es wird unter anderem gezeigt, dass man bei konjunktiven Grammatiken die Vereinigungsoperation stark einschr{\"a}nken kann, ohne dabei die erzeugte Sprache zu {\"a}ndern. Außerdem werden bestimmte Schaltkreise untersucht, deren Gatter keine Wahrheitswerte sondern Mengen von Zahlen berechnen. F{\"u}r diese Schaltkreise wird das {\"A}quivalenzproblem betrachtet, also die Frage ob zwei gegebene Schaltkreise die gleiche Menge berechnen oder nicht. Es stellt sich heraus, dass, abh{\"a}ngig von den erlaubten Gattertypen, die Komplexit{\"a}t des {\"A}quivalenzproblems stark variiert und f{\"u}r verschiedene Komplexit{\"a}tsklassen vollst{\"a}ndig ist, also als (parametrisierter) Vertreter f{\"u}r diese Klassen stehen kann.},
  subject      = {Mehrkriterielle Optimierung},
  language  = {en}
}
@phdthesis{Boehler2005,
  author    = {B{\"o}hler, Elmar},
  title     = {Algebraic closures in complexity theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-16106},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2005},
  abstract  = {We use algebraic closures and structures which are derived from these in complexity theory. We classify problems with Boolean circuits and Boolean constraints according to their complexity. We transfer algebraic structures to structural complexity. We use the generation problem to classify important complexity classes.},
  subject      = {Komplexit{\"a}tstheorie},
  language  = {en}
}
@phdthesis{Reith2001,
  author    = {Reith, Steffen},
  title     = {Generalized Satisfiability Problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-74},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2001},
  abstract  = {In the last 40 years, complexity theory has grown to a rich and powerful field in theoretical computer science. The main task of complexity theory is the classification of problems with respect to their consumption of resources (e.g., running time or required memory). To study the computational complexity (i.e., consumption of resources) of problems, similar problems are grouped into so called complexity classes. During the systematic study of numerous problems of practical relevance, no efficient algorithm for a great number of studied problems was found. Moreover, it was unclear whether such algorithms exist. A major breakthrough in this situation was the introduction of the complexity classes P and NP and the identification of hardest problems in NP. These hardest problems of NP are nowadays known as NP-complete problems. One prominent example of an NP-complete problem is the satisfiability problem of propositional formulas (SAT). Here we get a propositional formula as an input and it must be decided whether an assignment for the propositional variables exists, such that this assignment satisfies the given formula. The intensive study of NP led to numerous related classes, e.g., the classes of the polynomial-time hierarchy PH, P, \#P, PP, NL, L and \#L. During the study of these classes, problems related to propositional formulas were often identified to be complete problems for these classes. Hence some questions arise: Why is SAT so hard to solve? Are there modifications of SAT which are complete for other well-known complexity classes? In the context of these questions a result by E. Post is extremely useful. He identified and characterized all classes of Boolean functions being closed under superposition. It is possible to study problems which are connected to generalized propositional logic by using this result, which was done in this thesis. Hence, many different problems connected to propositional logic were studied and classified with respect to their computational complexity, clearing the borderline between easy and hard problems.},
  subject      = {Erf{\"u}llbarkeitsproblem},
  language  = {en}
}
@phdthesis{Kosub2001,
  author    = {Kosub, Sven},
  title     = {Complexity and Partitions},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-2808},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2001},
  abstract  = {Computational complexity theory usually investigates the complexity of sets, i.e., the complexity of partitions into two parts. But often it is more appropriate to represent natural problems by partitions into more than two parts. A particularly interesting class of such problems consists of classification problems for relations. For instance, a binary relation R typically defines a partitioning of the set of all pairs (x,y) into four parts, classifiable according to the cases where R(x,y) and R(y,x) hold, only R(x,y) or only R(y,x) holds or even neither R(x,y) nor R(y,x) is true. By means of concrete classification problems such as Graph Embedding or Entailment (for propositional logic), this thesis systematically develops tools, in shape of the boolean hierarchy of NP-partitions and its refinements, for the qualitative analysis of the complexity of partitions generated by NP-relations. The Boolean hierarchy of NP-partitions is introduced as a generalization of the well-known and well-studied Boolean hierarchy (of sets) over NP. Whereas the latter hierarchy has a very simple structure, the situation is much more complicated for the case of partitions into at least three parts. To get an idea of this hierarchy, alternative descriptions of the partition classes are given in terms of finite, labeled lattices. Based on these characterizations the Embedding Conjecture is established providing the complete information on the structure of the hierarchy. This conjecture is supported by several results. A natural extension of the Boolean hierarchy of NP-partitions emerges from the lattice-characterization of its classes by considering partition classes generated by finite, labeled posets. It turns out that all significant ideas translate from the case of lattices. The induced refined Boolean hierarchy of NP-partitions enables us more accuratly capturing the complexity of certain relations (such as Graph Embedding) and a description of projectively closed partition classes.},
  subject      = {Partition <Mengenlehre>},
  language  = {en}
}
@phdthesis{Baier1998,
  author    = {Baier, Herbert},
  title     = {Operators of Higher Order},
  publisher = {Shaker Verlag},
  isbn      = {3-8265-4008-5},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-140799},
  school      = {Universit{\"a}t W{\"u}rzburg},
  pages     = {V, 95},
  year      = {1998},
  abstract  = {Motivated by results on interactive proof systems we investigate the computational power of quantifiers applied to well-known complexity classes. In special, we are interested in existential, universal and probabilistic bounded error quantifiers ranging over words and sets of words, i.e. oracles if we think in a Turing machine model. In addition to the standard oracle access mechanism, we also consider quantifiers ranging over oracles to which access is restricted in a certain way.},
  subject      = {Komplexit{\"a}tstheorie},
  language  = {en}
}