Related papers: Knuth-Bendix algorithm and the conjugacy problems …
Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…
The basic method of rewriting for words in a free monoid given a monoid presentation is extended to rewriting for paths in a free category given a `Kan extension presentation'. This is related to work of Carmody-Walters on the Todd-Coxeter…
We propose a new cryptosystem based on polycyclic groups. The cryptosystem is based on the fact that the word problem can be solved effectively in polycyclic groups, while the known solutions to the conjugacy problem are far less efficient.
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical…
With a view on applications in computing, in particular concurrency theory and higher-dimensional rewriting, we develop notions of $n$-fold monoid and comonoid objects in $n$-fold monoidal categories and bicategories. We present a series of…
We show thatthe double reversing algorithm proposed by dehornoy for solving the word problem in the braid group can also be used to recognize the conjugates of powers of the generators in an Artin group of spherical type. The proof uses a…
In this work we describe a method to reconstruct the braid monodromy of the preimage of a curve by a Kummer cover. This method is interesting, since it combines two techniques, namely, the reconstruction of a highly non-generic braid…
We study the properties, in particular termination, of dependent types systems for lambda calculus and rewriting.
In this note we solve the twisted conjugacy problem for braid groups, i.e. we propose an algorithm which, given two braids $u,v\in B_n$ and an automorphism $\phi \in Aut (B_n)$, decides whether $v=(\phi (x))^{-1}ux$ for some $x\in B_n$. As…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
The Benders' decomposition algorithm is a technique in mathematical programming for complex mixed-integer linear programming (MILP) problems with a particular block structure. The strategy of Benders' decomposition can be described as a…
A modification of Merino-Mi\v{c}ka-M\"utze's solution to a combinatorial generation problem of Knuth is proposed in this survey. The resulting alternate form to such solution is compatible with a reinterpretation by the author of a proof of…
Quantum lambda calculus has been studied mainly as an idealized programming language -- the evaluation essentially corresponds to a deterministic abstract machine. Very little work has been done to develop a rewriting theory for quantum…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Recently the third named author defined a 2-parametric family of groups $G_n^k$ \cite{gnk}. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups $G_n^k$ and dynamical systems…
We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed subgroups of free group automorphisms, and one…
In this paper we investigate convergent term rewriting systems that conform to the criteria set out by Christopher Lynch and Barbara Morawska in their seminal paper "Basic Syntactic Mutation." The equational unification problem modulo such…
A bicategory approach to differential cohomology is presented. Based on the axioms of Bunke-Schick, a symmetric monoidal groupoid is associated to differential refinements of cohomology theories. It is proven that such differential…
It is shown how to use a small finite state automaton in two variables in order to carry out the Knuth-Bendix process for rewriting words in a group in shortlex order. The two-variable automaton can be used to store an infinite set of rules…
Let $M$ be a positive homogeneously presented monoid ${\langle L \mid R\,\rangle}_{mo}$. If $M$ satisfies the cancellation condition and carries certain particular elements similar to the \emph{fundamental elements} in Artin monoids, then…