Related papers: A Generalized Concurrent Rule Construction for Dou…
Model-driven software engineering is a suitable method for dealing with the ever-increasing complexity of software development processes. Graphs and graph transformations have proven useful for representing such models and changes to them.…
We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…
We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in a non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is a…
In this paper we introduce a new clustering technique called Regularity Clustering. This new technique is based on the practical variants of the two constructive versions of the Regularity Lemma, a very useful tool in graph theory. The…
An alternative foundation for 2-categories is explored by studying graph-theoretically a partial operation on 2-cells named juncture, which can replace vertical and horizontal composition. Juncture is a generalized vertical composition of…
Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can…
A common problem of classical neural network architectures is that additional information or expert knowledge cannot be naturally integrated into the learning process. To overcome this limitation, we propose a two-step approach consisting…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
Recent studies have highlighted the limitations of large language models in mathematical reasoning, particularly their inability to capture the underlying logic. Inspired by meta-learning, we propose that models should acquire not only…
Cut-elimination theorems constitute one of the most important classes of theorems of proof theory. Since Gentzen's proof of the cut-elimination theorem for the system $\mathbf{LK}$, several other proofs have been proposed. Even though the…
Multi-task learning leverages potential correlations among related tasks to extract common features and yield performance gains. However, most previous works only consider simple or weak interactions, thereby failing to model complex…
The competition graph of a directed acyclic graph D is the undirected graph on the same vertex set as D in which two distinct vertices are adjacent if they have a common out-neighbor in D. The competition number of an undirected graph G is…
In this paper we focus on concurrent processes built on synchronization by means of futures. This concept is an abstraction for processes based on a main execution thread but allowing to delay some computations. The structure of a general…
Machine learning relies on the assumption that unseen test instances of a classification problem follow the same distribution as observed training data. However, this principle can break down when machine learning is used to make important…
Adhesive categories provide an abstract framework for the algebraic approach to rewriting theory, where many general results can be recast and uniformly proved. However, checking that a model satisfies the adhesivity properties is sometimes…
We introduce two-crossing elections as a generalization of single-crossing elections, showing a number of new results. First, we show that two-crossing elections can be recognized in polynomial time, by reduction to the well-studied…
We present a general framework for carrying out some constructions. The unifying factor is a combinatorial principle which we present in terms of a game in which the first player challenges the second player to carry out constructions which…
We develop a rewriting theory suitable for diagrammatic algebras and lay down the foundations of a systematic study of their higher structures. In this paper, we focus on the question of finding bases. As an application, we give the first…
Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…
Graph-structured data is ubiquitous in practice and often processed using graph neural networks (GNNs). With the adoption of recent laws ensuring the ``right to be forgotten'', the problem of graph data removal has become of significant…