Related papers: Coherence of string rewriting systems by decreasin…
This article is concerned with automating the decreasing diagrams technique of van Oostrom for establishing confluence of term rewrite systems. We study abstract criteria that allow to lexicographically combine labelings to show local…
We consider the problem of binary string reconstruction from the multiset of its substring compositions, i.e., referred to as the substring composition multiset, first introduced and studied by Acharya et al. We introduce a new algorithm…
We present a methodology for proving termination of left-linear term rewriting systems (TRSs) by using Albert Burroni's polygraphs, a kind of rewriting systems on algebraic circuits. We translate the considered TRS into a polygraph of…
For the lambda-calculus with surjective pairing and terminal type, Curien and Di Cosmo were inspired by Knuth-Bendix completion, and introduced a confluent rewriting system that (1) extends the naive rewriting system, and (2) is stable…
String diagrams are pictorial representations for morphisms of symmetric monoidal categories. They constitute an intuitive and expressive graphical syntax, which has found application in a very diverse range of fields including concurrency…
We introduce homotopical methods based on rewriting on higher-dimensional categories to prove coherence results in categories with an algebraic structure. We express the coherence problem for (symmetric) monoidal categories as an…
In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…
Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or discarded at will. In SMTs, traditional tree-like terms are…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
In this paper, we introduce monoidal rewriting systems (MRS), an abstraction of string rewriting in which reductions are defined over an arbitrary ambient monoid rather than a free monoid of words. This shift is partly motivated by logic:…
Beginning with a review of the arguments leading to the so-called c=1 barrier in the continuum formulation of noncritical string theory, the pathology is then exhibited in a discretized version of the theory, formulated through dynamical…
String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and…
We study the confluence property of abstract rewriting systems internal to cubical categories. We introduce cubical contractions, a higher-dimensional generalisation of reductions to normal forms, and employ them to construct cubical…
We investigate the structure and reconstruction complexity of Manacher arrays. First, we establish a combinatorial lower bound, proving that the number of rooted tandem repeat trees with $n+1$ genes exceeds the number of distinct Manacher…
This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation…
We explore the Collatz conjecture and its variants through the lens of termination of string rewriting. We construct a rewriting system that simulates the iterated application of the Collatz function on strings corresponding to mixed…
A coherent presentation of an n-category is a presentation by generators, relations and relations among relations. Confluent and terminating rewriting systems generate coherent presentations, whose relations among relations are defined by…
Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an…
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However,…
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…