Related papers: Simulations, Computations, and Statistics for Long…

Variable Length Memory Chains (VLMC), which are generalizations of finite order Markov chains, turn out to be an essential tool to modelize random sequences in many domains, as well as an interesting object in contemporary probability…

In this work, we consider a variant of the classical Longest Common Subsequence problem called Doubly-Constrained Longest Common Subsequence (DC-LCS). Given two strings s1 and s2 over an alphabet A, a set C_s of strings, and a function Co…

The expected length of longest common subsequences is a problem that has been in the literature for at least twenty five years. Determining the limiting constants \gamma_k appears to be quite difficult, and the current best bounds leave…

A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can…

Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…

We consider a general class of super-additive scores measuring the similarity of two independent sequences of $n$ i.i.d. letters from a finite alphabet. Our object of interest is the mean score by letter $l_n$. By the subadditivity $l_n$ is…

Let $X_1,X_2,\ldots$ and $Y_1,Y_2,\ldots$ be two random sequences so that every random variable takes values in a finite set $\mathbb{A}$. We consider a global similarity score $L_n:=L(X_1,\ldots,X_n;Y_1,\ldots,Y_n)$ that measures the…

The {\em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. Palindrome is a word which reads the same forward as it does backward. The {\em longest common palindromic subsequence (LCPS)}…

As increasingly sophisticated language models emerge, their trustworthiness becomes a pivotal issue, especially in tasks such as summarization and question-answering. Ensuring their responses are contextually grounded and faithful is…

Overlapping frequently occurs in paired texts in natural language processing tasks like text editing and semantic similarity evaluation. Better evaluation of the semantic distance between the overlapped sentences benefits the language…

One of the most critical problems in the field of string algorithms is the longest common subsequence problem (LCS). The problem is NP-hard for an arbitrary number of strings but can be solved in polynomial time for a fixed number of…

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n,…

Semantic Textual Similarity (STS) is the basis of many applications in Natural Language Processing (NLP). Our system combines convolution and recurrent neural networks to measure the semantic similarity of sentences. It uses a convolution…

Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…

Contrast-Consistent Search (CCS) is an unsupervised probing method able to test whether large language models represent binary features, such as sentence truth, in their internal activations. While CCS has shown promise, its two-term…

Labelled Markov chains (LMCs) are widely used in probabilistic verification, speech recognition, computational biology, and many other fields. Checking two LMCs for equivalence is a classical problem subject to extensive studies, while the…

Capturing the interdependencies between real valued time series can be achieved by finding common similar patterns. The abstraction of time series makes the process of finding similarities closer to the way as humans do. Therefore, the…

Calculating the semantic similarity between sentences is a long dealt problem in the area of natural language processing. The semantic analysis field has a crucial role to play in the research related to the text analytics. The semantic…

The longest common subsequence (LCS) is a fundamental problem in string processing which has numerous algorithmic studies, extensions, and applications. A sequence $u_1, \ldots, u_f$ of $f$ strings s said to be an ($f$-)segmentation of a…