Related papers: The monoid of queue actions
We study conjugacy relations on semigroups and monoids, focusing on the relation $a \cfn b$, defined by the existence of $g,h \in S^1$ such that $ag = gb$, $bh = ha$, $hag = b$, and $gbh = a$. This notion emerged as one that yields…
In computer science, especially when dealing with quantum computing or other non-standard models of computation, basic notions in probability theory like "a predicate" vary wildly. There seems to be one constant: the only useful example of…
We continue our programme of extending key techniques from geometric group theory to semigroup theory, by studying monoids acting by isometric embeddings on spaces equipped with asymmetric, partially-defined distance functions. The…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…
In this paper we study modular tensor categories (braided rigid balanced tensor categories with additional finiteness and non-degeneracy conditions), in particular, representations of quantum groups at roots of unity. We show that the…
In many situations one encounters an entity that resembles a monoid. It consists of a carrier and two operations that resemble a unit and a multiplication, subject to three equations that resemble associativity and left and right unital…
Consider the set $M_{a,b} = \{n \in \mathbb Z_{\ge 1} : n \equiv a \bmod b\} \cup \{1\}$ for $a, b \in \mathbb Z_{\ge 1}$. If $a^2 \equiv a \bmod b$, then $M_{a,b}$ is closed under multiplication and known as an arithmetic congruence monoid…
Organizations continuously accumulate data, often according to some business processes. If one poses a query over such data for decision support, it is important to know whether the query is stable, that is, whether the answers will stay…
We study the globalization problem for a strong partial action $\alpha$ of a monoid $M$ on a semigroup $X$ via the associated rewriting system $(X_M^+,\to)$. We show that the local confluence of $(X_M^+,\to)$ is sufficient for the…
The algebraic variety defined by the idempotents of an incidence monoid is investigated. Its irreducible components are determined. The intersection with an antichain submonoid is shown to be the union of these irreducible components. The…
We consider Turing machines as actions over configurations in $\Sigma^{\mathbb{Z}^d}$ which only change them locally around a marked position that can move and carry a particular state. In this setting we study the monoid of Turing machines…
We define computational atoms named "actions" equipped primarily with three operations: reduction, collection, and inspection. We show how actions can be used for decision-making algorithms from simple axioms. We describe the encodings of…
Ordered, linear, and other substructural type systems allow us to expose deep properties of programs at the syntactic level of types. In this paper, we develop a family of unary logical relations that allow us to prove consequences of…
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…
A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show…
In this paper, we consider the inverse submonoids $AM_n$ of monotone transformations and $AO_n$ of order-preserving transformations of the alternating inverse monoid $AI_n$ on a chain with $n$ elements. We compute the cardinalities,…
The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy…
We study some of the factorization invariants of the class of Puiseux monoids generated by geometric sequences, and we compare and contrast them with the known results for numerical monoids generated by arithmetic sequences. The class we…
Subsets of a matrix algebra over a field that are invariant under conjugation and contain the linear span of each two of their commuting elements are described. They obviously include the subsets of diagonalizable and nilpotent matrices. In…