Learn 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 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)
Dedicated to the memory of Des Sheiham, our inspiring instructor, valued colleague and great friend Abstract. We give a combinatorial classification of postsingu-larly 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(More)
We give a combinatorial classification of postsingu-larly 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 postsingu-larly finite exponential maps given(More)
Dedicated to the memory of Des Sheiham, our inspiring instructor, valued colleague and great friend Abstract. We give a combinatorial classification of postsingu-larly 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(More)
  • 1