Related papers: The subword reversing method
Machine learning is applied to find proofs, with smaller or smallest numbers of nodes, for the classification of 4-nilpotent semigroups.
This work lists and describes the main recent strategies for building fixed-length, dense and distributed representations for words, based on the distributional hypothesis. These representations are now commonly called word embeddings and,…
Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their…
Taxonomy construction is not only a fundamental task for semantic analysis of text corpora, but also an important step for applications such as information filtering, recommendation, and Web search. Existing pattern-based methods extract…
A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of…
The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of…
Cayley's theorem tells us that all groups $\mathbf{G}$ occur as subgroups of the group of automorphisms over some set $X$. In this paper we consider a `sort-of' converse to this question: given a set $X$ and some transformation group…
The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A finite semigroup embeds in a real hyperplane face monoid if…
In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding…
Let $G = \mathrm{SL}(n,\mathbb{C})$, let $B$ be a fixed Borel subgroup, and let $P \supset B$ be a parabolic subgroup determined by a composition $(c_1,\dots,c_k)$ of $n$. Write $P'$ for the derived group of $P$ and $\mathfrak{m}$ for the…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
Pre-trained word embeddings improve the performance of a neural model at the cost of increasing the model size. We propose to benefit from this resource without paying the cost by operating strictly at the sub-lexical level. Our approach is…
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…
First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field.…
We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
The word problem for discrete groups is well-known to be undecidable by a Turing Machine; more precisely, it is reducible both to and from and thus equivalent to the discrete Halting Problem. The present work introduces and studies a real…
A superredundant clause is a clause that is redundant in the resolution closure of a formula. The converse concept of superirredundancy ensures membership of the clause in all minimal CNF formulae that are equivalent to the given one. This…
Language model based methods are powerful techniques for text classification. However, the models have several shortcomings. (1) It is difficult to integrate human knowledge such as keywords. (2) It needs a lot of resources to train the…
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…