Related papers: Minimal Absent Words on Run-Length Encoded Strings
A reduced word of a permutation $w$ is a minimal length expression of $w$ as a product of simple transpositions. We examine the computational complexity, formulas and (randomized) algorithms for their enumeration. In particular, we prove…
Large language models achieve breakthroughs in complex reasoning via long chain-of-thought sequences. However, this often leads to severe reasoning inflation, causing substantial computational redundancy. To maximize Intelligence per Token,…
A bit catastrophe, loosely defined, is when a change in just one character of a string causes a significant change in the size of the compressed string. We study this phenomenon for the Burrows-Wheeler Transform (BWT), a string transform at…
Large Language Models have proven highly successful at modelling a variety of tasks. However, this comes at a steep computational cost that hinders wider industrial uptake. In this paper, we present MWT: a Multi-Word Tokenizer that goes…
In a \emph{weighted sequence}, for every position of the sequence and every letter of the alphabet a probability of occurrence of this letter at this position is specified. Weighted sequences are commonly used to represent imprecise or…
In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to…
Multiword expressions (MWEs) present groups of words in which the meaning of the whole is not derived from the meaning of its parts. The task of processing MWEs is crucial in many natural language processing (NLP) applications, including…
Given a string $T$ of length $n$, a substring $u = T[i..j]$ of $T$ is called a shortest unique substring (SUS) for an interval $[s,t]$ if (a) $u$ occurs exactly once in $T$, (b) $u$ contains the interval $[s,t]$ (i.e. $i \leq s \leq t \leq…
The compact directed acyclic word graph (CDAWG) is the minimal compact automaton that recognizes all the suffixes of a string. Classically the CDAWG has been implemented as an index of the string it recognizes, requiring $o(n)$ space for a…
Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that…
Automated Compliance Checking (ACC) systems aim to semantically parse building regulations to a set of rules. However, semantic parsing is known to be hard and requires large amounts of training data. The complexity of creating such…
Word embedding has become an essential means for text-based information retrieval. Typically, word embeddings are learned from large quantities of general and unstructured text data. However, in the domain of music, the word embedding may…
The Minimum Linear Arrangement problem (MLA) consists of finding a mapping $\pi$ from vertices of a graph to distinct integers that minimizes $\sum_{\{u,v\}\in E}|\pi(u) - \pi(v)|$. In that setting, vertices are often assumed to lie on a…
If $w=u\alpha$ for $\alpha\in \Sigma=\{1,2\}$ and $u\in \Sigma^*$, then $w$ is said to be a \textit{simple right extension}of $u$ and denoted by $u\prec w$. Let $k$ be a positive integer and $P^k(\epsilon)$ denote the set of all…
In this work, we propose a novel and efficient minimum word error rate (MWER) training method for RNN-Transducer (RNN-T). Unlike previous work on this topic, which performs on-the-fly limited-size beam-search decoding and generates…
The problem of dictionary matching is a classical problem in string matching: given a set S of d strings of total length n characters over an (not necessarily constant) alphabet of size sigma, build a data structure so that we can match in…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…
Given a sequence composed of a limit number of characters, we try to "read" it as a "text". This involves to segment the sequence into "words". The difficulty is to distinguish good segmentation from enormous number of random ones.Aiming at…
We study the IS-algorithm, a well-known linear-time algorithm for computing the suffix array of a word. This algorithm relies on transforming the input word $w$ into another word, called the reduced word of $w$, that will be at least twice…
We propose regular expression inference (REI) as a challenge for code/language modelling, and the wider machine learning community. REI is a supervised machine learning (ML) and program optimisation task, and poses the problem of finding…