Related papers: Reduction Operators and Completion of Rewriting Sy…
We introduce the notion of syzygy for a set of reduction operators and relate it to the notion of syzygy for presentations of algebras. We give a method for constructing a linear basis of the space of syzygies for a set of reduction…
We propose a functional description of rewriting systems on topological vector spaces. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting…
The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system:…
We write a procedure for constructing noncommutative Groebner bases. Reductions are done by particular linear projectors, called reduction operators. The operators enable us to use a lattice construction to reduce simultaneously each…
The purpose of this article is to propose and investigate a partial order structure weaker than the lattice structure and which have nice properties regarding closure operators. We extend accordingly closed pattern mining and formal concept…
Considering patterns as sets of their instances, a difference operator over patterns computes a finite set of two given patterns, which represents the difference between the dividend pattern and the divisor pattern. A complement of a…
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…
In this paper we apply the methods of rewriting systems and Gr\"obner-Shirshov bases to give a unified approach to a class of linear operators on associative algebras. These operators resemble the classic Rota-Baxter operator, and they are…
Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly…
Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A…
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
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,…
A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. We define a class of bases called…
Logically constrained term rewriting is a relatively new rewriting formalism that naturally supports built-in data structures, such as integers and bit vectors. In the analysis of logically constrained term rewrite systems (LCTRSs),…
We consider partial and total reduction of a nonhomogeneous linear system of the operator equations with the system matrix in the same particular form as in paper [N. Shayanfar, M. Hadizadeh 2013]. Here we present two different concepts.…
We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give an alternative description of the lattice of all subvarieties…
On an infinite set some closure operators are finitary (algebraic) while others are not. We can generalize this idea for a complete algebraic lattice letting the compact elements act as the finite sets. With this in mind, we will consider…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
Deduction systems and graph rewriting systems are compared within a common categorical framework. This leads to an improved deduction method in diagrammatic logics.