Symmetry within Solutions

We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to solution symmetry, which is a mapping between different solutions of the same problem. We argue that we may be able to exploit both types of symmetry when finding solutions. We illustrate the potential of exploiting internal symmetries on two benchmark domains: Van der Waerden numbers and graceful graphs. By identifying internal symmetries we are able to extend the state of the art in both cases.Comment: AAAI 2010, Proceedings of Twenty-Fourth AAAI Conference on Artificial Intelligenc

QRAT+: Generalizing QRAT by a More Powerful QBF Redundancy Property

The QRAT (quantified resolution asymmetric tautology) proof system simulates virtually all inference rules applied in state of the art quantified Boolean formula (QBF) reasoning tools. It consists of rules to rewrite a QBF by adding and deleting clauses and universal literals that have a certain redundancy property. To check for this redundancy property in QRAT, propositional unit propagation (UP) is applied to the quantifier free, i.e., propositional part of the QBF. We generalize the redundancy property in the QRAT system by QBF specific UP (QUP). QUP extends UP by the universal reduction operation to eliminate universal literals from clauses. We apply QUP to an abstraction of the QBF where certain universal quantifiers are converted into existential ones. This way, we obtain a generalization of QRAT we call QRAT+. The redundancy property in QRAT+ based on QUP is more powerful than the one in QRAT based on UP. We report on proof theoretical improvements and experimental results to illustrate the benefits of QRAT+ for QBF preprocessing.Comment: preprint of a paper to be published at IJCAR 2018, LNCS, Springer, including appendi

The genetics of sexual development in East African cichlid fishes

Sexual development leads to the formation of males and females. This process can be controlled genetically, environmentally or by a combination thereof. Genetic sex determination is based on single- or polygenic actions, either linked to sex chromosomes or independent from them, while environmental sex determination includes factors such as temperature, density or social status. Teleost fishes, as the most species-rich clade of vertebrates, feature an overwhelming diversity of sex-determining mechanisms. In contrast to most mammals, where the presence or absence of one single gene defines the sexual fate, several master sex regulators have been identified in fish. Together with the description of complex polygenic regulations and the discovery of new functions of presumably conserved down-stream factors, fish exhibit a greater plasticity in generating males and females than previously thought. East African cichlid fishes are extremely diverse in terms of ecology, morphology and breeding behavior and therefore represent a prime model system in evolutionary biology in general, and in the study of sexual development in particular. Several sex determination systems have been described, which differ sometimes even between closely related species in this fish family. In my thesis, I investigated a set of candidate genes for sexual development in cichlids. More specifically, we studied these genes in adult cichlid species and in one of them also during early male development. Differential gene expression patterns, measured in brain and gonad tissue, were observed between cichlid lineages and within the same species over time. One striking case is the shift in gene expression of the aromatase cyp19a1. In vertebrates, and in all teleosts investigated so far, cyp19a1A and cyp19a1B are expressed in the ovaries and the brain, respectively. In the species rich and extremely diverse haplochromine lineage, we found an overexpression of cyp19a1B in the testis. In another study, we show that Astatotilapia burtoni, a member haplochromine lineage, most likely has an XX-XY sex determination system. Making use of hormonally sex-reversed fish and subsequent crossing experiments, we establish all-male broods, which offered an ideal platform to investigate gene expression of early testis and brain genes. In addition, we identified several promising candidates for genetic sex determiners in this species

Efficient Certified Resolution Proof Checking

We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms a state-of-the-art checker by two orders of magnitude. We then formalize the theory underlying propositional proof checking in Coq, and extract a correct-by-construction proof checker for our format from the formalization. An empirical evaluation using 280 unsatisfiable instances from the 2015 and 2016 SAT competitions shows that this certified checker usually performs comparably to a state-of-the-art non-certified proof checker. Using this format, we formally verify the recent 200 TB proof of the Boolean Pythagorean Triples conjecture