Related papers: Free operated monoids and Rewriting systems
We describe a generic construction of non-wellfounded syntax involving variable binding and its monadic substitution operation. Our construction of the syntax and its substitution takes place in category theory, notably by using monoidal…
Long before we learn to construct the field of rational numbers (out of the ring of integers) at university, we learn how to calculate with fractions at school. When it comes to "numbers", we are used to a commutative multiplication, for…
We introduce a new algebraic construction, {\em monop}, that combines monoids (with respect to the product of species), and operads (monoids with respect to the substitution of species) in the same algebraic structure. By the use of…
We present a new semiclassical technique which relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold…
Quorum systems are a powerful mechanism for ensuring the consistency of replicated data. Production systems usually opt for majority quorums due to their simplicity and fault tolerance, but majority quorum systems provide poor throughput…
The total right ring of quotients $Q_{\mathrm{tot}}^r(R),$ sometimes also called the maximal flat epimorphic right ring of quotients or right flat epimorphic hull, is usually obtained as a directed union of a certain family of extension of…
Monads can be interpreted as encoding formal expressions, or formal operations in the sense of universal algebra. We give a construction which formalizes the idea of "evaluating an expression partially": for example, "2+3" can be obtained…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
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…
The purpose of this paper is to extend some useful results, such as the multiplication being open, previously known for suitable finitely generated relatively free profinite semigroups, to relatively free profinite semigroupoids over…
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…
Every $F$-inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $\sigma$-class. In this enriched signature, the class of all $F$-inverse monoids forms a variety of algebraic…
The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work…
An operadic framework is developed to explain the inversion formula relating moments and cumulants in operator-valued free probability theory.
One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of…
Although in general there is no meaningful concept of factorization in fields, that in free associative algebras (over a commutative field) can be extended to their respective free field (universal field of fractions) on the level of…
We study congruences on the partial automorphism monoid of a finite rank free group action. We give a decomposition of a congruence on this monoid into a Rees congruence, a congruence on a Brandt semigroup and an idempotent separating…
We show how to construct a family of groups with simple commutator subgroups from aperiodic 1-vertex, finitely aligned higher rank graphs (which are, in fact, a class of cancellative monoids). Inverse semigroups form the intermediary…
Abstract. This article determines relations between two notions concerning monoids: factorability structure, introduced to simplify the bar complex; and quadratic normalisation, introduced to generalise quadratic rewriting systems and…
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…