Related papers: Rewriting Systems on Arbitrary Monoids
Let $(A,\m)$ be a Noetherian local ring, let $M$ be a finitely generated \CM $A$-module of dimension $r \geq 2$ and let $I$ be an ideal of definition for $M$. Set $L^I(M) = \bigoplus_{n\geq 0}M/I^{n+1}M$. In part one of this paper we showed…
In Multi-Document Summarization (MDS), the input can be modeled as a set of documents, and the output is its summary. In this paper, we focus on pretraining objectives for MDS. Specifically, we introduce a novel pretraining objective, which…
This paper outlines a theoretical framework using which different automatic metrics can be designed for evaluation of Machine Translation systems. It introduces the concept of {\em cognitive ease} which depends on {\em adequacy} and {\em…
In this work, we propose new variants of Anderson acceleration and nonlinear GMRES for general fixed-point iterations, based on modified least-squares problems associated with the methods. To solve the underlying linear systems, we apply…
We describe a modular rewriting system for translating optimization problems written in a domain-specific language to forms compatible with low-level solver interfaces. Translation is facilitated by reductions, which accept a category of…
We present a constructive formalization of Abstract Rewriting Systems (ARS) in the Agda proof assistant, focusing on standard results in term rewriting. We define a taxonomy of concepts related to termination and confluence and investigate…
Initial semantics aims to capture inductive structures and their properties as initial objects in suitable categories. We focus on the initial semantics aiming to model the syntax and substitution structure of programming languages with…
We initiate the study of higher dimensional topological finiteness properties of monoids. This is done by developing the theory of monoids acting on CW complexes. For this we establish the foundations of $M$-equivariant homotopy theory…
In this paper we establish an automated amortised resource analysis for term rewrite systems. The method is presented in an annotated type system and gives rise to polynomial bounds on the innermost runtime complexity of the analysed term…
Adhesive and quasiadhesive categories provide a general framework for the study of algebraic graph rewriting systems. In a quasiadhesive category any two regular subobjects have a join which is again a regular subobject. Vice versa, if…
We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous…
Readability-controlled text simplification (RCTS) rewrites texts to lower readability levels while preserving their meaning. RCTS models often depend on parallel corpora with readability annotations on both source and target sides. Such…
Successfully handling context is essential for any dialog understanding task. This context maybe be conversational (relying on previous user queries or system responses), visual (relying on what the user sees, for example, on their screen),…
The proliferation of retrieval-augmented generation (RAG) has established vector databases as critical infrastructure, yet they introduce severe privacy risks via embedding inversion attacks. Existing paradigms face a fundamental trade-off:…
In Natural Language Processing, multi-document summarization (MDS) poses many challenges to researchers above those posed by single-document summarization (SDS). These challenges include the increased search space and greater potential for…
There are many evaluation strategies for term rewrite systems, but proving termination automatically is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies full termination. We adapt…
Text summarization is an interesting area for researchers to develop new techniques to provide human like summaries for vast amounts of information. Summarization techniques tend to focus on providing accurate representation of content, and…
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…
We show that given a finitely generated standard-graded algebra of dimension $d$ over an infinite field, its graded Noether normalizations obey a certain kind of `generic exchange', allowing one to pass between any two of them in at most…
This paper presents a new approach of automatic text summarization which combines domain oriented text analysis (DoTA) and rhetorical structure theory (RST) in a grammar form: the attributed rhetorical structure grammar (ARSG), where the…