Related papers: Knuth-Bendix algorithm and the conjugacy problems …
We give an algorithm to solve the Conjugacy Problem for ascending HNN-extensions of free groups. To do this, we give algorithms to solve certain problems on dynamics of free group endomorphisms.
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
This paper discusses various types of constraints, difficulties and solutions to overcome the challenges regarding university course allocation problem. A hybrid evolutionary algorithm has been defined combining Local Repair Algorithm and…
Let $n\geq 3$. In this paper we deal with the conjugacy problem in the Artin braid group quotient $B_n/[P_n,P_n]$. To solve it we use systems of equations over the integers arising from the action of $B_n/[P_n,P_n]$ over the abelianization…
In analogy to the disjoint cycle decomposition in permutation groups, Ore and Specht define a decomposition of elements of the full monomial group and exploit this to describe conjugacy classes and centralisers of elements in the full…
We give several algorithms addressing computations of intersections of conjugate subgroups.
Residuation theory concerns the study of partially ordered algebraic structures, most often monoids, equipped with a weak inverse for the monoidal operator. One of its area of application has been constraint programming, whose key…
Clustering is a commonplace problem in many areas of data science, with applications in biology and bioinformatics, understanding chemical structure, image segmentation, building recommender systems, and many more fields. While there are…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
We present an algorithm for solving the conjugacy search problem in the four strand braid group. The computational complexity is cubic with respect to the braid length.
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
The balanced incomplete block design (BIBD) problem is a difficult combinatorial problem with a large number of symmetries, which add complexity to its resolution. In this paper, we propose a dual (integer) problem representation that…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
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…
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…
We summarize the main known results involving subword reversing, a method of semigroup theory for constructing van Kampen diagrams by referring to a preferred direction. In good cases, the method provides a powerful tool for investigating…
In this paper, we show how to extend the notion of reducibility introduced by Girard for proving the termination of $\beta$-reduction in the polymorphic $\lambda$-calculus, to prove the termination of various kinds of rewrite relations on…
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…
We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include…
A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved…