Related papers: The Algebras for Automatic Relations
We introduce pseudoalgebras for relative pseudomonads and develop their theory. For each relative pseudomonad $T$, we construct a free--forgetful relative pseudoadjunction that exhibits the bicategory of $T$-pseudoalgebras as terminal among…
Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the well-known applications…
In this work, we introduce a semi-algebraic model for automatic parallelization of perfectly nested polynomial loops, which generalizes the classical polyhedral model. This model supports the basic tasks for automatic loop parallelization,…
We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…
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…
In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…
In this paper, we study the machine learning elements which we are interested in together as a machine learning system, consisting of a collection of machine learning elements and a collection of relations between the elements. The…
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to the one of equational classes defined by equation arrows. Free…
This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over $C((x))$ and $\mathbb P^1_C\smallsetminus\{0,\infty\}$, where $C$ is…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…
We propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of…
Automata admitting at most one accepting run per structure, known as unambiguous automata, find applications in verification of reactive systems as they extend the class of deterministic automata whilst maintaining some of their desirable…
Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles. In an academic collaboration network, for example,…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…
Conjunctive table algebras are introduced and axiomatically characterized. A conjunctive table algebra is a variant of SPJR algebra (a weaker form of relational algebra), which corresponds to conjunctive queries with equality. The table…
Pseudoalgebras, introduced in [BDK], are multi-dimensional analogues of conformal algebras, which provide an axiomatic description of the singular part of the operator product expansion. Our main interest in this paper is the pseudoalgebra…
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…
The class of finitely presented algebras over a field K with a set of generators a_1,...,a_n and defined by homogeneous relations of the form a_1a_2...a_n = a_{sigma(1)}a_{sigma(2)}...a_{sigma(n)}, where sigma runs through an abelian…