Related papers: A Generalized Next-Closure Algorithm -- Enumeratin…
We introduce an algorithm for computing closure systems derived from a family of implications on a set. Semilattices presentations are explored and used in conjunction with the algorithm to compute various types of lattices freely generated…
We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…
In this article, we present a new data type agnostic algorithm calculating a concept lattice from heterogeneous and complex data. Our NextPriorityConcept algorithm is first introduced and proved in the binary case as an extension of…
We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum (maximum) element, these generalized ideals turn into ordinary (dual) ideals.
The purpose of this article is to propose and investigate a partial order structure weaker than the lattice structure and which have nice properties regarding closure operators. We extend accordingly closed pattern mining and formal concept…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.
We generalize a well-known algorithm for the generation of all subsets of a set in lexicographic order with respect to the sets as lists of elements (subset-lex order). We obtain algorithms for various combinatorial objects such as the…
A specialization semilattice is a semilattice together with a coarser preorder satisfying a compatibility condition. We show that the category of specialization semilattices is isomorphic to the category of semilattices with a congruence,…
A specialization semilattice is a join semilattice together with a coarser preorder $ \sqsubseteq $ satisfying an appropriate compatibility condition. If $X$ is a topological space, then $(\mathcal P(X), \cup, \sqsubseteq )$ is a…
We study centralizer clones of finite lattices and semilattices. For semilattices, we give two characterizations of the centralizer and also derive formulas for the number of operations of a given essential arity in the centralizer. We also…
A topologized semilattice $X$ is called complete if each non-empty chain $C\subset X$ has $\inf C$ and $\sup C$ that belong to the closure $C$ of the chain $C$ in $X$. In this paper, we introduce various concepts of completeness of…
Many (but not all) approaches self-qualifying as "meta-learning" in deep learning and reinforcement learning fit a common pattern of approximating the solution to a nested optimization problem. In this paper, we give a formalization of this…
In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from the theories of groups, automata, and inverse semigroups.…
To represent anything from mathematical concepts to real-world objects, we have to resort to an encoding. Encodings, such as written language, usually assume a decoder that understands a rich shared code. A semantic embedding is a form of…
We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give an alternative description of the lattice of all subvarieties…
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
A specialization semilattice is a structure which can be embedded into $(\mathcal P(X), \cup, \sqsubseteq )$, where $X$ is a topological space, $ x \sqsubseteq y$ means $x \subseteq Ky$, for $x,y \subseteq X$, and $K$ is closure in $X$.…
We provide algorithms for performing computations in generalized numerical semigroups, that is, submonoids of $\mathbb{N}^{d}$ with finite complement in $\mathbb{N}^{d}$. These semigroups are affine semigroups, which in particular implies…
This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.
We present an algorithm for the optimization of a class of finite element integration loop nests. This algorithm, which exploits fundamental mathematical properties of finite element operators, is proven to achieve a locally optimal…