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Quantified Boolean formulas (QBFs) play an important role in theoretical computer science. QBF extends propositional logic in such a way that many advanced forms of reasoning can be easily formulated and evaluated. In this dissertation we present our ZQSAT, which is an algorithm for evaluating quantified Boolean formulas. ZQSAT is based on ZBDD: Zero-Suppressed Binary Decision Diagram , which is a variant of BDD, and an adopted version of the DPLL algorithm. It has been implemented in C using the CUDD: Colorado University Decision Diagram package. The capability of ZBDDs in storing sets of subsets efficiently enabled us to store the clauses of a QBF very compactly and let us to embed the notion of memoization to the DPLL algorithm. These points led us to implement the search algorithm in such a way that we could store and reuse the results of all previously solved subformulas with a little overheads. ZQSAT can solve some sets of standard QBF benchmark problems (known to be hard for DPLL based algorithms) faster than the best existing solvers. In addition to prenex-CNF, ZQSAT accepts prenex-NNF formulas. We show and prove how this capability can be exponentially beneficial.
Modern biological analysis techniques supply scientists with various forms of data. One category of such data are the so called "expression data". These data indicate the quantities of biochemical compounds present in tissue samples. Recently, expression data can be generated at a high speed. This leads in turn to amounts of data no longer analysable by classical statistical techniques. Systems biology is the new field that focuses on the modelling of this information. At present, various methods are used for this purpose. One superordinate class of these methods is machine learning. Methods of this kind had, until recently, predominantly been used for classification and prediction tasks. This neglected a powerful secondary benefit: the ability to induce interpretable models. Obtaining such models from data has become a key issue within Systems biology. Numerous approaches have been proposed and intensively discussed. This thesis focuses on the examination and exploitation of one basic technique: decision trees. The concept of comparing sets of decision trees is developed. This method offers the possibility of identifying significant thresholds in continuous or discrete valued attributes through their corresponding set of decision trees. Finding significant thresholds in attributes is a means of identifying states in living organisms. Knowing about states is an invaluable clue to the understanding of dynamic processes in organisms. Applied to metabolite concentration data, the proposed method was able to identify states which were not found with conventional techniques for threshold extraction. A second approach exploits the structure of sets of decision trees for the discovery of combinatorial dependencies between attributes. Previous work on this issue has focused either on expensive computational methods or the interpretation of single decision trees a very limited exploitation of the data. This has led to incomplete or unstable results. That is why a new method is developed that uses sets of decision trees to overcome these limitations. Both the introduced methods are available as software tools. They can be applied consecutively or separately. That way they make up a package of analytical tools that usefully supplement existing methods. By means of these tools, the newly introduced methods were able to confirm existing knowledge and to suggest interesting and new relationships between metabolites.
Subject of this work is the study of applications of the Galactic Microlensing effect, where the light of a distant star (source) is bend according to Einstein's theory of gravity by the gravitational field of intervening compact mass objects (lenses), creating multiple (however not resolvable) images of the source. Relative motion of source, observer and lens leads to a variation of deflection/magnification and thus to a time dependant observable brightness change (lightcurve), a so-called microlensing event, lasting weeks to months. The focus lies on the modeling of binary-lens events, which provide a unique tool to fully characterize the lens-source system and to detect extra-solar planets around the lens star. Making use of the ability of genetic algorithms to efficiently explore large and intricate parameter spaces in the quest for the global best solution, a modeling software (Tango) for binary lenses is developed, presented and applied to data sets from the PLANET microlensing campaign. For the event OGLE-2002-BLG-069 the 2nd ever lens mass measurement has been achieved, leading to a scenario, where a G5III Bulge giant at 9.4 kpc is lensed by an M-dwarf binary with total mass of M=0.51 solar masses at distance 2.9 kpc. Furthermore a method is presented to use the absence of planetary lightcurve signatures to constrain the abundance of extra-solar planets.