Related papers: Termination orders for 3-dimensional rewriting

We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…

This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…

We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…

In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence…

This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form…

A rewriting system is a set of equations over a given set of terms called rules that characterize a system of computation and is a powerful general method for providing decision procedures of equational theories, based upon the principle of…

In this article, we propose a finite volume limiter function for a reconstruction on the three-point stencil. Compared to classical limiter functions in the MUSCL framework, which yield $2^{\text{nd}}$-order accuracy, the new limiter is…

Recent work has proven that training large language models with self-supervised tasks and fine-tuning these models to complete new tasks in a transfer learning setting is a powerful idea, enabling the creation of models with many…

A graph is reconstructible if it is determined up to isomorphism by the multiset of its proper induced subgraphs. The reconstruction conjecture postulates that every graph of order at least 3 is reconstructible. We show that interval graphs…

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…

We present a Haskell library for first-order term rewriting covering basic operations on positions, terms, contexts, substitutions and rewrite rules. This effort is motivated by the increasing number of term rewriting tools that are written…

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…

Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a…

Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages,…

We generalize the notion of identities among relations, well known for presentations of groups, to presentations of n-categories by polygraphs. To each polygraph, we associate a track n-category, generalizing the notion of crossed module…

In engineering practice one often encounters planar problems, where the corresponding vector space of forces, velocities or (infinitesimal) displacements is three dimensional. This paper shows how these spaces can be factorized, such that…

This paper investigates the learning of 3rd-order tensors representing the semantics of transitive verbs. The meaning representations are part of a type-driven tensor-based semantic framework, from the newly emerging field of compositional…

The Size-Change Termination principle was first introduced to study the termination of first-order functional programs. In this work, we show that it can also be used to study the termination of higher-order rewriting in a system of…

In this article, we mainly give the strictly copositive conditions of a special class of third order three dimensional symmetric tensors. More specifically, by means of the polynomial decomposition method, the analytic sufficient and…

We describe several technical tools that prove to be efficient for investigating the rewrite systems associated with a family of algebraic laws, and might be useful for more general rewrite systems. These tools consist in introducing a…