Related papers: An example of goal-directed, calculational proof
We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
It is well known by analysts that a concept lattice has an exponential size in the data. Thus, as soon as he works with real data, the size of the concept lattice is a fundamental problem. In this chapter, we propose to investigate factor…
A binary relation defined on a poset is a weakening relation if the partial order acts as a both-sided compositional identity. This is motivated by the weakening rule in sequent calculi and closely related to models of relevance logic. For…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…
In this paper we show how to combine two algorithmic techniques to obtain linear time algorithms for various optimization problems on graphs, and present a subroutine which will be useful in doing so. The first technique is iterative…
We use edge slidings and saturated disjoint Borel families to give a conceptually simple proof of Hjorth's theorem on cost attained: if a countable p.m.p. ergodic equivalence relation $E$ is treeable and has cost $n \in \mathbb{N} \cup…
Similarity learning is a general problem to elicit useful representations by predicting the relationship between a pair of patterns. This problem is related to various important preprocessing tasks such as metric learning, kernel learning,…
The relationship between two important problems in tree pattern matching, the largest common subtree and the smallest common supertree problems, is established by means of simple constructions, which allow one to obtain a largest common…
In the present paper we consider the problem of constructing all the projective rooted spanning trees of a given graph. We propose an algorithm based on reducing this problem to the problem of constructing all the maximal independent sets…
The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…
Our paper is the first study of what one might call "reverse mathematics of explicit fixpoints". We study two methods of constructing such fixpoints for formulas whose principal connective is the intuitionistic Lewis arrow. Our main…
Many graph embedding approaches have been proposed for knowledge graph completion via link prediction. Among those, translating embedding approaches enjoy the advantages of light-weight structure, high efficiency and great interpretability.…
Suppose we wish to embed an (associative) $k$-algebra $A$ in a $k$-algebra $R$ generated in some specified way; e.g., by two elements, or by copies of given $k$-algebras $A_1,$ $A_2,$ $A_3.$ Several authors have obtained sufficient…
A landmark result from rational approximation theory states that $x^{1/p}$ on $[0,1]$ can be approximated by a type-$(n,n)$ rational function with root-exponential accuracy. Motivated by the recursive optimality property of Zolotarev…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that…
An important example of a multi-dimensional integrable system is the anti-self-dual Einstein equations. By studying the symmetries of these equations, a recursion operator is found and the associated hierarchy constructed. Owing to the…
Tilings of the plane resemble the simplicial and other complexes from algebraic topology, but have not been studied from this perspective. We construct finite categories corresponding to polygons with labeled directed edges, and introduce…