Related papers: Bounded Languages Described by GF(2)-grammars

Let $\Gamma$ be a generic subgroup of the multiplicative group $\mathbb{C}^*$ of nonzero complex numbers. We define a class of Lie algebras associated to $\Gamma$, called twisted $\Gamma$-Lie algebras, which is a natural generalization of…

Linear conjunctive grammars are a family of formal grammars with an explicit conjunction operation allowed in the rules, which is notable for its computational equivalence fo one-way real-time cellular automata, also known as trellis…

Ambiguity is ubiquitous in natural language. Resolving ambiguous meanings is especially important in information retrieval tasks. While word embeddings carry semantic information, they fail to handle ambiguity well. Transformer models have…

We obtain a family of new combinatorial identities for symmetric formal power series.

Let $k_1,k_2$ be two fields of characteristic 0. Let $G_1$ be a split semisimple algebraic group over $k_1$, $G_2$ a split Kac--Moody group over $k_2$ and $\phi\colon G_1(k_1)\to G_2(k_2)$ an abstract embedding. We show that $\im \phi$ is a…

In this paper, we prove certain multiplicity one theorems and define twisted gamma factors for irreducible generic cuspidal representations of split $G_2$ over finite fields $k$ of odd characteristic. Then we prove the first converse…

Constraint-based grammars can, in principle, serve as the major linguistic knowledge source for both parsing and generation. Surface generation starts from input semantics representations that may vary across grammars. For many declarative…

Grammar refers to the system of rules that governs the structural organization and the semantic relations among linguistic units such as sentences, phrases, and words within a given language. In natural language processing, there remains a…

Stabler proposes an implementation of the Chomskyan Minimalist Program, Chomsky 95 with Minimalist Grammars - MG, Stabler 97. This framework inherits a long linguistic tradition. But the semantic calculus is more easily added if one uses…

We propose the use of hyperedge replacement graph grammars for factor graphs, or factor graph grammars (FGGs) for short. FGGs generate sets of factor graphs and can describe a more general class of models than plate notation, dynamic…

The paper demonstrates the non-closure of the family of unambiguous linear languages (that is, those defined by unambiguous linear context-free grammars) under complementation. To be precise, a particular unambiguous linear grammar is…

Recently the third named author defined a 2-parametric family of groups $G_n^k$ \cite{gnk}. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups $G_n^k$ and dynamical systems…

We study the semantic relationship between G\"odel-Dummett logic $\mathsf{GL}$ and bounded-depth-2 logic $\mathsf{BD_2}$, two well-known intermediate logics. While $\mathsf{GL}$ imposes linearity on Kripke frames, $\mathsf{BD_2}$ bounds…

Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that…

In this paper the representation of $A_{\kk}(2)$ algebra given by Daoud and Kibler [M.Daoud and M.Kibler, J.Phys.A 43 115303 (2010), 45 244036 (2012)] is investigated. It is shown that the new generators are necessary for consistency of the…

In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate infix-, prefix-, and suffix-closed languages (referred to as…

We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions…

Lambek Grammars (LG) are a computational modelling of natural language, based on non-commutative compositional types. It has been widely studied, especially for languages where the syntax plays a major role (like English). The goal of this…

Ulam words are binary words defined recursively as follows: the length-$1$ Ulam words are $0$ and $1$, and a binary word of length $n$ is Ulam if and only if it is expressible uniquely as a concatenation of two shorter, distinct Ulam words.…

Graph Interpolation Grammars are a declarative formalism with an operational semantics. Their goal is to emulate salient features of the human parser, and notably incrementality. The parsing process defined by GIGs incrementally builds a…