Related papers: Remarks on separating words
A sequence of geometric random variables of length $n$ is a sequence of $n$ independent and identically distributed geometric random variables ($\Gamma_1, \Gamma_2, \dots, \Gamma_n$) where $\mathbb{P}(\Gamma_j=i)=pq^{i-1}$ for…
The Lexical Access Problem consists of determining the intended sequence of words corresponding to an input sequence of phonemes (basic speech sounds) that come from a low-level phoneme recognizer. In this paper we present an…
Grammatical inference consists in learning a language or a grammar from data. In this paper, we consider a number of models for inferring a non-deterministic finite automaton (NFA) with 3 sorts of states, that must accept some words, and…
We study the separability problem for automatic relations (i.e., relations on finite words definable by synchronous automata) in terms of recognizable relations (i.e., finite unions of products of regular languages). This problem takes as…
The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. A word (pattern) over a finite set is said to be unavoidable if, for all but finitely many words, there exists a morphism mapping…
We consider various shuffling and unshuffling operations on languages and words, and examine their closure properties. Although the main goal is to provide some good and novel exercises and examples for undergraduate formal language theory…
A closed word (a.k.a. periodic-like word or complete first return) is a word whose longest border does not have internal occurrences, or, equivalently, whose longest repeated prefix is not right special. We investigate the structure of…
Language models provide a key framework for studying linguistic theories based on prediction, but phonological analysis using large language models (LLMs) is difficult; there are few phonological benchmarks beyond English and the standard…
We study the distribution of spacings between the fractional parts of $n^d\alpha$. For $\alpha$ of high enough Diophantine type we prove a necessary and sufficient condition for $n^d\alpha\mod 1, 1\leq n\leq N,$ to be Poissonian as $N\to…
A minimal absent word of a sequence x, is a sequence yt hat is not a factorof x, but all of its proper factors are factors of x as well. The set of minimal absent words uniquely defines the sequence itself. In recent times minimal absent…
The field of speech separation, addressing the "cocktail party problem", has seen revolutionary advances with DNNs. Speech separation enhances clarity in complex acoustic environments and serves as crucial pre-processing for speech…
We introduced the notation of a set of prohibitions and give definitions of a complete set and a crucial word with respect to a given set of prohibitions. We consider 3 particular sets which appear in different areas of mathematics and for…
The inverse relationship between the length of a word and the frequency of its use, first identified by G.K. Zipf in 1935, is a classic empirical law that holds across a wide range of human languages. We demonstrate that length is one…
A word $w$ is called synchronizing (recurrent, reset, magic, directable) word of deterministic finite automaton (DFA) if $w$ sends all states of the automaton to a unique state. In 1964 Jan \v{C}erny found a sequence of n-state complete DFA…
$\textit{Partial words}$ are words that contain, in addition to letters, special symbols $\diamondsuit$ called $\textit{holes}$. Two partial words of $a=a_0 \dots a_n$ and $b=b_0 \dots b_n$ are $\textit{compatible}$ if for all $i$, $a_i =…
Non-native speakers show difficulties with spoken word processing. Many studies attribute these difficulties to imprecise phonological encoding of words in the lexical memory. We test an alternative hypothesis: that some of these…
We study the new problem of Huffman-like codes subject to individual restrictions on the code-word lengths of a subset of the source words. These are prefix codes with minimal expected code-word length for a random source where additionally…
Word embeddings provide an unsupervised way to understand differences in word usage between discursive communities. A number of recent papers have focused on identifying words that are used differently by two or more communities. But word…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
At present, most Natural Language Processing technology is based on the results of Word Segmentation for Dependency Parsing, which mainly uses an end-to-end method based on supervised learning. There are two main problems with this method:…