Related papers: Quadratic normalisation in monoids
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…
Renormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations, or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length,…
Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid…
Inverse braid monoid describes a structure on braids where the number of strings is not fixed. So, some strings of initial $n$ may be deleted. In the paper we show that many properties and objects based on braid groups may be extended to…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
We describe standard forms for elements of the higher-dimensional Thompson groups $nV$ arising from gridding subdivision processes. These processes lead to standard normal form descriptions for elements in these groups, and sizes of these…
This article deals with the notion of factorability. Elements of a factorable group or monoid possess a normal form, which leads to a small complex homotopy equivalent to its bar complex, thus computing its homology. We investigate the…
We investigate the monoid of transformations that are induced by sequences of writing to and reading from a queue storage. We describe this monoid by means of a confluent and terminating semi-Thue system and study some of its basic…
We introduce the notion of general prints of a word, which is substantialized by certain canonical decompositions, to study repetition in words. These associated decompositions, when applied recursively on a word, result in what we term as…
The aim of this note is to prove that monoids $\mathrm{Mon}\langle a,b:aUb=b\rangle$, with $aUb$ of relative length 6, admit finite complete rewriting systems. This is some advance in the understanding the long-standing open problem whether…
We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…
We study combinatorial inequalities for various classes of set systems: matroids, polymatroids, poset antimatroids, and interval greedoids. We prove log-concavity inequalities for counting certain weighted feasible words, which generalize…
In this paper we consider the normalized lengths of the factors of some factorizations of random words. First, for the \emph{Lyndon factorization} of finite random words with $n$ independent letters drawn from a finite or infinite totally…
We study the reduction in a lambda-calculus derived from Moggi's computational one, that we call the computational core. The reduction relation consists of rules obtained by orienting three monadic laws. Such laws, in particular…
Monoids generated by elements of order two appear in numerous places in the literature. For example, Coxeter reflection groups in geometry, Kuratowski monoids in topology, various monoids generated by regular operations in language theory…
We study numerically and analytically the average length of reduced (primitive) words in so-called locally free and braid groups. We consider the situations when the letters in the initial words are drawn either without or with…
Recently, metric learning and similarity learning have attracted a large amount of interest. Many models and optimisation algorithms have been proposed. However, there is relatively little work on the generalization analysis of such…
Computing normal forms in groups (or monoids) is in general harder than solving the word problem (equality testing). However, normal form computation has a much wider range of applications. It is therefore interesting to investigate the…
Abductive reasoning is a non-monotonic formalism stemming from the work of Peirce. It describes the process of deriving the most plausible explanations of known facts. Considering the positive version asking for sets of variables as…