Related papers: Weak Bases of Boolean Co-Clones
We are given a set of elements in a metric space. The distribution of the elements is arbitrary, possibly adversarial. Can we weigh the elements in a way that is resistant to such (adversarial) manipulations? This problem arises in various…
We give a formal treatment of simple type theories, such as the simply-typed $\lambda$-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional…
The notion of commutation of operations in universal algebra leads to the concept of centralizer clone and gives rise to a well-known class of problems that we call centralizer problems, in which one seeks to determine whether a given set…
We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…
We study the representation of non-weakly compact operators between $AL$-spaces. In this setting, we show that every operator admits a best approximant in the ideal of weakly compact operators. Using duality arguments, we extend this result…
A clone on a set X is a set of finitary operations on X which contains all projections and which is moreover closed under functional composition. Ordering all clones on X by inclusion, one obtains a complete algebraic lattice, called the…
The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.
We introduce the notion of clone algebra, intended to found a one-sorted, purely algebraic theory of clones. Clone algebras are defined by true identities and thus form a variety in the sense of universal algebra. The most natural clone…
The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. We consider bounds for the length and the height of the terms expressing these functions,…
The connection between constraint languages and clone theory has been a fruitful line of research on the complexity of constraint satisfaction problems. In a recent result, Cohen et al. [SICOMP'13] have characterised a Galois connection…
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have…
A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but non-positive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems. The…
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…
Weakly Schreier split extensions are a reasonably large, yet well-understood class of monoid extensions, which generalise some aspects of split extensions of groups. This short note provides a way to define and study similar classes of…
We develop a new general framework for algebras and clones, called Universal Clone Algebra. Algebras and clones of finitary operations are to Universal Algebra what t-algebras and clone algebras are to Universal Clone Algebra. Clone…
A fundamental fact for the algebraic theory of constraint satisfaction problems (CSPs) over a fixed template is that pp-interpretations between at most countable \omega-categorical relational structures have two algebraic counterparts for…
We determine the atoms of the interval of the clone lattice consisting of those clones which contain all permutations, on an infinite base set. This is equivalent to the description of the atoms of the lattice of transformation monoids…
Algebra bundles, in the strict sense, appear in many areas of geometry and physics. However, the structure of an algebra is flexible enough to vary non-trivially over a connected base, giving rise to a structure of a weak algebra bundle. We…
We give a short, self-contained, and elementary proof of the strong law of large numbers under a power law decay hypothesis for joint second moments. The result is related to the classical one by Lyons. However, we also provide a rate of…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…