Related papers: Non-simplifying Graph Rewriting Termination
Classical graph algorithms work well for combinatorial problems that can be thoroughly formalized and abstracted. Once the algorithm is derived, it generalizes to instances of any size. However, developing an algorithm that handles complex…
Graph decompositions are the natural generalisation of tree decompositions where the decomposition tree is replaced by a genuine graph. Recently they found theoretical applications in the theory of sparsity, topological graph theory,…
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…
Knowledge graphs are structured representations of facts in a graph, where nodes represent entities and edges represent relationships between them. Recent research has resulted in the development of several large KGs. However, all of them…
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…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
Natural language processing is an important discipline with the aim of understanding text by its digital representation, that due to the diverse way we write and speak, is often not accurate enough. Our paper explores different…
We prove that every graph which admits a tree-decomposition into finite parts has a rooted tree-decomposition into finite parts that is linked, tight and componental. As an application, we obtain that every graph without half-grid minor has…
Summarization of long sequences into a concise statement is a core problem in natural language processing, requiring non-trivial understanding of the input. Based on the promising results of graph neural networks on highly structured data,…
Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of…
This paper presents a tree-to-tree transduction method for sentence compression. Our model is based on synchronous tree substitution grammar, a formalism that allows local distortion of the tree topology and can thus naturally capture…
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…
Text simplification is one of the domains in Natural Language Processing (NLP) that offers an opportunity to understand the text in a simplified manner for exploration. However, it is always hard to understand and retrieve knowledge from…
In this paper we investigate convergent term rewriting systems that conform to the criteria set out by Christopher Lynch and Barbara Morawska in their seminal paper "Basic Syntactic Mutation." The equational unification problem modulo such…
We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree…
This paper studies the computational complexity of disambiguation under probabilistic tree-grammars and context-free grammars. It presents a proof that the following problems are NP-hard: computing the Most Probable Parse (MPP) from a…
Graph neural networks (GNNs) have become a popular approach to integrating structural inductive biases into NLP models. However, there has been little work on interpreting them, and specifically on understanding which parts of the graphs…
We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some…
Large Language Models are increasingly used by students to explore advanced material in computer science, including graph theory. As these tools become integrated into undergraduate and graduate coursework, it is important to understand how…
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…