A general parametric scheme of hierarchical clustering procedures with invariance under monotone transformations of similarity values and invariance under numeration of objects is described. This scheme consists of two steps: correction of given similarity values between objects and transitive closure of obtained valued relation. Some theoretical properties of considered scheme are studied. Dif...

A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin(v), such that u reaches v iff Lout(u) ∩ Lin(v) 6= ∅. Despite their simplicity and elegance, reachability oracles have failed to achieve efficiency in more than ten years since their introduction: The main problem is high construction cost, which stems from a set-cover framework and the need to ma...

Under the axiom of choice, every first countable space is a FréchetUrysohn space. Although, in its absence even R may fail to be a sequential space. Our goal in this paper is to discuss under which set-theoretic conditions some topological classes, such as the first countable spaces, the metric spaces or the subspaces of R, are classes of Fréchet-Urysohn or sequential spaces. In this context, i...

We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke’s result for Kripke models. Both the other two results are based on the properties of bisimulation invariance, compactness, and a third property: ω-bisimilarity, and expressive closure at level ω, respectively....

In this note we provide a concise report on the complexity of the causal ordering problem, originally introduced by Simon to reason about causal dependencies implicit in systems of mathematical equations. We show that Simon’s classical algorithm to infer causal ordering is NP-Hard—an intractability previously guessed but never proven. We present then a detailed account based on Nayak’s suggeste...

A tournament is a complete directed graph. A convex subset is a vertex subset with the property that every two-path beginning and ending inside the convex subset is contained completely within the subset. This paper shows a relationship between convex subsets and transitive closures which leads to an optimal O(n 3)-time algorithm for nding all convex subsets in a tournament.

A computer implementation of Gödel’s algorithm for class formation in Mathematica was used to formulate definitions and theorems about iteration in Gödel’s class theory. The intent is to use this approach for automated reasoning about a variety of applications of iteration using McCune’s automated reasoning program Otter. The applications include the theory of transitive closures of relations, ...

The nested relational algebra is often inadequate as a tool to handle nested relations, since several important queries, such as transitive closure, cannot expressed by it. On the other hand, the powerset algebra does allow the expression of transitive closure, but in a too expensive way. Therefore, we consider various other extensions to the nested algebra, such as least tixpoint and programmi...

Content Management Systems in the field of content production and publishing need to monitor the progress of large numbers of simultaneously evolving workflows. In order to make such systems adaptive to the varying needs of their organizations, the utilization of a graphical editor for workflows has been proposed, thus generating the hazard of the specification of erroneous and invalid workflow...

Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we describe an efficient algorithm for computing the transitive closures of difference bounds, octagonal and finite monoid affine relations. On the theoretical side, this framework provides a common solution to the acceleration problem, for all these three classes of r...