Related papers: Confluence of Layered Rewrite Systems
We present a new overlay, called the {\em Deterministic Decentralized tree} ($D^2$-tree). The $D^2$-tree compares favourably to other overlays for the following reasons: (a) it provides matching and better complexities, which are…
We present crest, a tool for automatically proving (non-)confluence and termination of logically constrained rewrite systems. We compare crest to other tools for logically constrained rewriting. Extensive experiments demonstrate the promise…
We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary…
We propose a method combining relational-logic representations with neural network learning. A general lifted architecture, possibly reflecting some background domain knowledge, is described through relational rules which may be handcrafted…
Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We…
We define a mapping from transition-based parsing algorithms that read sentences from left to right to sequence labeling encodings of syntactic trees. This not only establishes a theoretical relation between transition-based parsing and…
An important problem in phylogenetics is the construction of phylogenetic trees. One way to approach this problem, known as the supertree method, involves inferring a phylogenetic tree with leaves consisting of a set $X$ of species from a…
The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…
In the unidimensional unfolding model, given m objects in general position there arise 1+m(m-1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. By changing these m objects, we can generate various…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
A typical complex system should be described by a supernetwork or a network of networks, in which the networks are coupled to some other networks. As the first step to understanding the complex systems on such more systematic level,…
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…
Multi-task learning has been observed by many researchers, which supposes that different tasks can share a low-rank common yet latent subspace. It means learning multiple tasks jointly is better than learning them independently. In this…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
Dominant sequence models like the Transformer represent structure implicitly through dense attention weights, incurring quadratic complexity. We propose RewriteNets, a novel neural architecture built on an alternative paradigm: explicit,…
We prove "untyping" theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the…
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…
Online learning to rank is a core problem in machine learning. In Lattimore et al. (2018), a novel online learning algorithm was proposed based on topological sorting. In the paper they provided a set of self-normalized inequalities (a) in…
Recently, contrastive learning has risen to be a promising approach for large-scale self-supervised learning. However, theoretical understanding of how it works is still unclear. In this paper, we propose a new guarantee on the downstream…
In this paper, we consider an approach introduced in term rewriting for the automatic detection of non-looping non-termination from patterns of rules. We adapt it to logic programming by defining a new unfolding technique that produces…