Related papers: Confluence of Layered Rewrite Systems
A method is given that "inverts" a logic grammar and displays it from the point of view of the logical form, rather than from that of the word string. LR-compiling techniques are used to allow a recursive-descent generation algorithm to…
The goal of text ranking is to generate an ordered list of texts retrieved from a corpus in response to a query. Although the most common formulation of text ranking is search, instances of the task can also be found in many natural…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
We define a notion of rank for words and subshifts that we call spacer rank, extending the notion of rank-one symbolic shifts of Gao and Hill. We construct infinite words of each finite spacer rank, of unbounded spacer rank, and show there…
This paper describes a novel method of compiling ranked tagging rules into a deterministic finite-state device called a bimachine. The rules are formulated in the framework of regular rewrite operations and allow unrestricted regular…
We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…
We introduce a pointfree theory of convergence on lattices and coframes. A convergence lattice is a lattice $L$ with a monotonic map $\lim_L$ from the lattice of filters on $L$ to $L$, meant to be an abstract version of the map sending…
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…
While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where…
Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…
We prove that a group is presented by finite convergent length-reducing rewriting systems where each rule has left-hand side of length 3 if and only if the group is plain. Our proof goes via a new result concerning properties of embedded…
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…
We use a labelled deduction system based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type. We also define a term rewriting system that is used to make computations between these…
Natural language is hierarchically structured: smaller units (e.g., phrases) are nested within larger units (e.g., clauses). When a larger constituent ends, all of the smaller constituents that are nested within it must also be closed.…
Text clustering holds significant value across various domains due to its ability to identify patterns and group related information. Current approaches which rely heavily on a computed similarity measure between documents are often limited…
Ranking systems produce ordered lists from scalar scores, yet the ranking itself depends only on pairwise comparisons. We develop a mathematical theory that takes this observation seriously, centering the analysis on pairwise margins rather…
This note presents a method of interpreting the tree adjoining languages as the natural third step in a hierarchy that starts with the regular and the context-free languages. The central notion in this account is that of a higher-order…
String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is…
We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…
Cyclic words are equivalence classes of cyclic permutations of ordinary words. When a group is given by a rewriting relation, a rewriting system on cyclic words is induced, which is used to construct algorithms to find minimal length…