Related papers: Solutions to twisted word equations and equations …
We present a new evolution system for Einstein's field equations which is based on tetrad fields and conformally compactified hyperboloidal spatial hypersurfaces which reach future null infinity. The boost freedom in the choice of the…
We first construct a linear basis for a free metabelian Poisson algebra generated by an arbitrary well-ordered set. It turns out that such a linear basis depends on the characteristic of the underlying field. Then we elaborate the method of…
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We…
We develop a family of techniques to align word embeddings which are derived from different source datasets or created using different mechanisms (e.g., GloVe or word2vec). Our methods are simple and have a closed form to optimally rotate,…
For two given $\omega$-terms $\alpha$ and $\beta$, the word problem for $\omega$-terms over a variety $\boldsymbol{\mathrm{V}}$ asks whether $\alpha=\beta$ in all monoids in $\boldsymbol{\mathrm{V}}$. We show that the word problem for…
In 2018, it was shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is still an open problem as to where to precisely place the word problems of hyperbolic groups in the formal…
We study ergodic-theoretic properties of coded shift spaces. A coded shift space is defined as a closure of all bi-infinite concatenations of words from a fixed countable generating set. We derive sufficient conditions for the uniqueness of…
We consider the Noether's problem on the noncommutative real rational functions invariant under the linear action of a finite group. For abelian groups the invariant skew-fields are always rational. We show that for a solvable group the…
We prove new complexity results for computational problems in certain wreath products of groups and (as an application) for free solvable group. For a finitely generated group we study the so-called power word problem (does a given…
Based on [1], we study the complexity of horizontality in each twistor space $\hat{E}_{\varepsilon}$ associated with an oriented vector bundle $E$ of rank $4$ with a positive-definite metric over the $2$-torus $T^2$, and obtain…
We analyze a class of linear wave equations for odd half spin that have a well posed initial value problem. We demonstrate consistency of the equations in curved space-times. They generalize the Weyl neutrino equation. We show that there…
A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced…
There are many open questions surrounding the characterisation of groups with context-sensitive word problem. Only in 2018 was it shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is…
For a finite connected graph $\mathcal{E}$ with set of edges $E$, a finite $E$-generated group $G$ is constructed such that the set of relations $p=1$ satisfied by $G$ (with $p$ a word over $E\cup E^{-1}$) is closed under deletion of…
In this paper, we initiate the study of the twisted weak order associated to a twisted Bruhat order for a Coxeter group and explore the relationship between the lattice property of such order and the infinite reduced words. We show that for…
Let $G$ be a group, and let $S$ be a finite subset of $G$ that generates $G$ as a monoid. The co-word problem is the collection of words in the free monoid $S^{\ast}$ that represent non-trivial elements of $G$. A current conjecture, based…
Automated theorem provers (ATPs) can disprove conjectures by saturating a set of clauses, but the resulting saturated sets are opaque certificates. In the unit equational fragment, a saturated set can in fact be read as a convergent rewrite…
We generalize the classical Post correspondence problem ($\mathbf{PCP}_n$) and its non-homogeneous variation ($\mathbf{GPCP}_n$) to non-commutative groups and study the computational complexity of these new problems. We observe that…
The set of idempotents of any semigroup carries the structure of a biordered set, which contains a great deal of information concerning the idempotent generated subsemigroup of the semigroup in question. This leads to the construction of a…
Textual open intent classification is crucial for real-world dialogue systems, enabling robust detection of unknown user intents without prior knowledge and contributing to the robustness of the system. While adaptive decision boundary…