Related papers: $\pi$-augmented pregroups and applications to ling…
Language transformations are algorithms that take a language specification in input, and return the language specification modified. Language transformations are useful for automatically adding features such as subtyping to programming…
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…
We formulate and explain the extended Burrows-Wheeler transform of Mantaci et al from the viewpoint of permutations on a chain taken as a union of partial order-preserving mappings. In so doing we establish a link with syntactic semigroups…
We show that normalizers and permutational isomorphisms of permutation groups given by generating sets can be computed in time simply exponential in the degree of the groups. The result is obtained by exploiting canonical forms for…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
Natural language inference (NLI) is among the most challenging tasks in natural language understanding. Recent work on unsupervised pretraining that leverages unsupervised signals such as language-model and sentence prediction objectives…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
For natural language processing systems, two kinds of evidence support the use of text representations from neural language models "pretrained" on large unannotated corpora: performance on application-inspired benchmarks (Peters et al.,…
We give new applications of graded Lie algebras to: identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, $2k$-Lie algebras, generalized Poisson brackets and so on.
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…
In this paper we suggest how the mathematical concept of hyperstructures may be a useful tool in the study of the higher, hierachical structure of languages.
This paper presents a model for linguistic description based on group theory. A grammar in this model, or "G-grammar", is a collection of lexical expressions which are products of logical forms, phonological forms, and their inverses.…
We study admissible transformations and Lie symmetries for a class of variable-coefficient Burgers equations. We combine the advanced methods of splitting into normalized subclasses and of mappings between classes that are generated by…
A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…
Our constructions provide a systematic way to study cohomology pre-algebraic structures via classical cohomology, simplifying computations and enabling the use of established techniques.
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
A novel approach to automated learning of syntactic rules governing natural languages is proposed, based on using probabilities assigned to sentences (and potentially longer word sequences) by transformer neural network language models to…
Various uses of the renormalization group are examined.
We describe a method of using statistically-collected Chinese character groups from a corpus to augment a Chinese dictionary. The method is particularly useful for extracting domain-specific and regional words not readily available in…
The method of preliminary group classification is rigorously defined, enhanced and related to the theory of group classification of differential equations. Typical weaknesses in papers on this method are discussed and strategies to overcome…