Related papers: Normal ordering problem and the extensions of the …
This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
We introduce regular languages of morphisms in free monoidal categories, with their associated grammars and automata. These subsume the classical theory of regular languages of words and trees, but also open up a much wider class of…
In this paper we consider a variant of the orthogonal range reporting problem when all points should be reported in the sorted order of their $x$-coordinates. We show that reporting two-dimensional points with this additional condition can…
We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score…
Positional numeration systems are a large family of numeration systems used to represent natural numbers. Whether the set of all representations forms a regular language or not is one of the most important questions that can be asked of…
The origin of complex structures, randomness, and irreversibility are analyzed in the scale free SL(2,R) analysis, which is an extension of the ordinary analysis based on the recently uncovered scale free $C^{2^n-1}$ solutions to linear…
We develop a nonstandard approach to exploring polynomials associated with peaks and runs of permutations. With the aid of a context-free grammar, or a set of substitution rules, one can perform a symbolic calculus, and the computation…
We define and study a spatial (infinite-dimensional) counterpart of Stirling numbers. In classical combinatorics, the Pochhammer symbol $(m)_n$ can be extended from a natural number $m\in\mathbb N$ to the falling factorials…
The aim of this paper is twofold. Firstly, we investigate a finite sum involving the generalized falling factorial polynomials, in some special cases of which we express it in terms of the degenerate Stirling numbers of the second kind, the…
We study a certain poset on the free monoid on a countable alphabet. This poset is determined by the fact that its total extensions are precisely the standard term orders. We also investigate the poset classifying degree-compatible standard…
In this work, we study the generalized sorting problem, where we are given a set of $n$ elements to be sorted, but only a subset of all possible pairwise element comparisons is allowed. We look at the problem from the perspective of the…
Synchronous Context-Free Grammars (SCFGs), also known as syntax-directed translation schemata, are unlike context-free grammars in that they do not have a binary normal form. In general, parsing with SCFGs takes space and time polynomial in…
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…
The aim of this paper is by using generating functions to further study some identities and properties on the degenerate Stirling numbers of the second kind, the degenerate $r$-Stirling numbers of the second kind, the degenerate Stirling…
It is well known that ascents, descents and plateaux are equidistributed over the set of classical Stirling permutations. Their common enumerative polynomials are the second-order Eulerian polynomials, which have been extensively studied by…
Generally, open string boundary conditions play a nontrivial role in string theory. For example, in the presence of an antisymmetric tensor background field, they will lead the spacetime coordinates noncommutative. In this paper, we mainly…
Existing works have studied the impacts of the order of words within natural text. They usually analyze it by destroying the original order of words to create a scrambled sequence, and then comparing the models' performance between the…
Grammatical inference is a classical problem in computational learning theory and a topic of wider influence in natural language processing. We treat grammars as a model of computation and propose a novel neural approach to induction of…
The increasingly widespread adoption of large language models has highlighted the need for improving their explainability. We present context length probing, a novel explanation technique for causal language models, based on tracking the…