Bastian Laubner

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We extend first-order logic with counting by a new operator that allows it to formalise a limited form of recursion which can be evaluated in logarithmic space. The resulting logic LREC has a data complexity in LOGSPACE, and it defines LOGSPACE-complete problems like deterministic reachability and Boolean formula evaluation. We prove that LREC is strictly(More)
We introduce extensions of first-order logic (FO) and fixed-point logic (FP) with operators that compute the rank of a definable matrix. These operators are generalizations of the counting operations in FP+C (i.e. fixed-point logic with counting) that allow us to count the dimension of a definable vector space, rather than just count the cardinality of a(More)
We present a logspace algorithm for computing a canonical labeling, in fact a canonical interval representation, for interval graphs. To achieve this, we compute canonical interval representations of interval hypergraphs. This approach also yields a canonical labeling of convex graphs. As a consequence, the isomorphism and automorphism problems for these(More)
We prove a characterization of all polynomialtime computable queries on the class of interval graphs by sentences of fixed-point logic with counting. More precisely, it is shown that on the class of unordered interval graphs, any query is polynomial-time computable if and only if it is definable in fixed-point logic with counting. This result is one of the(More)
We give a combinatorial classification of postsingularly finite exponential maps in terms of external addresses starting with the entry 0. This is an extension of the classification results for critically preperiodic polynomials [BFH] to exponential maps. Our proof relies on the topological characterization of postsingularly finite exponential maps given(More)
We give a combinatorial classification of postsingularly finite exponential maps in terms of external addresses starting with the entry 0. This is an extension of the classification results for critically preperiodic polynomials [BFH] to exponential maps. Our proof relies on the topological characterization of postsingularly finite exponential maps given(More)
We give a combinatorial classification of postsingularly finite exponential maps in terms of external addresses starting with the entry 0. This is an extension of the classification results for critically preperiodic polynomials [BFH] to exponential maps. Our proof relies on the topological characterization of postsingularly finite exponential maps given(More)
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