相关论文: 2D Lyndon Words and Applications
Contrary to several other families of lambda terms, no closed formula or generating function is known and none of the sophisticated techniques devised in analytic combinatorics can currently help with counting or generating the set of {\em…
A flip-swap language is a set S of binary strings of length n such that $S \cup 0^n$ is closed under two operations (when applicable): (1) Flip the leftmost 1; and (2) Swap the leftmost 1 with the bit to its right. Flip-swap languages model…
With sound unification, Definite Clause Grammars and compact expression of combinatorial generation algorithms, logic programming is shown to conveniently host a declarative playground where interesting properties and behaviors emerge from…
Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…
We study the fundamental problem of finding the best string to represent a given set, in the form of the Closest String problem: Given a set $X \subseteq \Sigma^d$ of $n$ strings, find the string $x^*$ minimizing the radius of the smallest…
This paper investigates the approximability of the Longest Common Subsequence (LCS) problem. The fastest algorithm for solving the LCS problem exactly runs in essentially quadratic time in the length of the input, and it is known that under…
An upward (resp. downward) digitally convex word is a binary word that best approximates from below (resp. from above) an upward (resp. downward) convex curve in the plane. We study these words from the combinatorial point of view,…
Bidimensionality is the most common technique to design subexponential-time parameterized algorithms on special classes of graphs, particularly planar graphs. The core engine behind it is a combinatorial lemma of Robertson, Seymour and…
We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has…
We review some recent results in digital geometry obtained by using a combinatorics on words approach to discrete geometry. Motivated on the one hand by the well-known theory of Sturmian words which model conveniently discrete lines in the…
The paper presents a linguistic and computational model aiming at making the morphological structure of the lexicon emerge from the formal and semantic regularities of the words it contains. The model is word-based. The proposed…
The notion of string attractor has been introduced in [Kempa and Prezza, 2018] in the context of Data Compression and it represents a set of positions of a finite word in which all of its factors can be "attracted". The smallest size…
The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…
We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In…
Recurrent Neural Network (RNN) is one of the most popular architectures used in Natural Language Processsing (NLP) tasks because its recurrent structure is very suitable to process variable-length text. RNN can utilize distributed…
An elastic-degenerate (ED) string is a sequence of $n$ sets of strings of total length $N$, which was recently proposed to model a set of similar sequences. The ED string matching (EDSM) problem is to find all occurrences of a pattern of…
A De Bruijn cycle is a cyclic sequence in which every word of length $n$ over an alphabet $\mathcal{A}$ appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words,…
Given a totally finite ordered alphabet $ A $, endowing the set of words over $ A $ with the alternating lexicographic order, we define a new class of Lyndon words. We study the fundamental properties of the associated symbolic dynamical…
Semantic search with large language models (LLMs) enables retrieval by meaning rather than keyword overlap, but scaling it requires major inference efficiency advances. We present LinkedIn's LLM-based semantic search framework for AI Job…
String diagrams are a graphical language used to represent processes that can be composed sequentially or in parallel, which correspond graphically to horizontal or vertical juxtaposition. In this paper we demonstrate how to compute the…