Related papers: Normal ordering problem and the extensions of the …
Existing entailment datasets mainly pose problems which can be answered without attention to grammar or word order. Learning syntax requires comparing examples where different grammar and word order change the desired classification. We…
Most natural languages have a predominant or fixed word order. For example in English the word order is usually Subject-Verb-Object. This work attempts to explain this phenomenon as well as other typological findings regarding word order…
This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
In a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials…
Ma-Ma-Yeh made a beautiful observation that a transformation of the grammar of Dumont instantly leads to the $\gamma$-positivity of the Eulerian polynomials. We notice that the transformed grammar bears a striking resemblance to the grammar…
Recently, the $\lambda$-analogues of $r$-Stirling numbers of the first kind were studied by Kim-Kim. The aim of this paper is to introduce the $\lambda$-analogues of $r$-Stirling numbers of the second kind and to investigate some…
This note presents a method of interpreting the tree adjoining languages as the natural third step in a hierarchy that starts with the regular and the context-free languages. The central notion in this account is that of a higher-order…
We consider context-free languages equipped with the lexicographic ordering. We show that when the lexicographic ordering of a context-free language is scattered, then its Hausdorff rank is less than $\omega^\omega$. As a corollary of this…
Morphological segmentation has traditionally been modeled with non-hierarchical models, which yield flat segmentations as output. In many cases, however, proper morphological analysis requires hierarchical structure -- especially in the…
Word ordering is a constrained language generation task taking unordered words as input. Existing work uses linear models and neural networks for the task, yet pre-trained language models have not been studied in word ordering, let alone…
In this study we introduce a second type of higher order generalised geometric polynomials. This we achieve by examining the generalised stirling numbers $S(n; k;\alpha;\beta;\gamma)$ [Hsu & Shiue,1998] for some negative arguments. We study…
We propose a new grammar-based language for defining information-extractors from documents (text) that is built upon the well-studied framework of document spanners for extracting structured data from text. While previously studied…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
In Combinatorics Stirling numbers may be defined in several ways. One such definition is given in [1], where an extensive consideration of Stirling numbers is presented. In this paper an alternative definition of Stirling numbers of both…
Word order is an important concept in natural language, and in this work, we study how word order affects the induction of world knowledge from raw text using language models. We use word analogies to probe for such knowledge. Specifically,…
Recently, several authors have studied the Stirling numbers of the second kind and Bell polynomials. In this paper, we study the extended Stirling polynomials of the second kind and the extended Bell polynomials associated with the Stirling…
Grounded language models use external sources of information, such as knowledge graphs, to meet some of the general challenges associated with pre-training. By extending previous work on compositional generalization in semantic parsing, we…
A $1$-prefix normal word is a binary word with the property that no factor has more $1$s than the prefix of the same length; a $0$-prefix normal word is defined analogously. These words arise in the context of indexed binary jumbled pattern…
Umbral extensions of the stirling numbers of the second kind are considered and the resulting dobinski-like various formulas including new ones are presented. These extensions naturally encompass the two well known q-extensions. The further…