Related papers: Church-Rosser Systems, Codes with Bounded Synchron…
A superimposed code is a collection of binary vectors (codewords) with the property that no vector is contained in the Boolean sum of any $k$ others, enabling unique identification of codewords within any group of $k$. Superimposed codes…
The problem of finding subfield subcodes of generalized Reed-Solomon (GRS) codes (i.e., alternant codes) is considered. A pure linear algebraic approach is taken in order to derive message constraints that generalize the well known…
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…
Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-gap statement says that for a structured set of words -- such…
Humans understand new combinations of words encountered if they are combinations of words recognized from different contexts, an ability called Compositional Generalization. The COGS benchmark (Kim and Linzen, 2020) arXiv:2010.05465 reports…
We introduce a new family of compressed data structures to efficiently store and query large string dictionaries in main memory. Our main technique is a combination of hierarchical Front-coding with ideas from longest-common-prefix…
Chronofold is a replicated data structure for versioned text. It is designed for use in collaborative editors and revision control systems. Past models of this kind either retrofitted local linear orders to a distributed system (the OT…
The material in this book is presented to graduate students in Information and Communication theory. The idea is that we give an introduction to particular applications of information theory and coding in digital communications. The goal is…
We design a Rocq library about adhesive categories, using Hierarchy Builder (HB). It is built around two hierarchies. The first is for categories, with usual categories at the bottom and adhesive categories at the top, with weaker variants…
The repair bandwidth of a code is the minimum amount of data required to repair one or several failed nodes (erasures). For MDS codes, the repair bandwidth is bounded below by the so-called cut-set bound, and codes that meet this bound with…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
Cross-lingual representations of words enable us to reason about word meaning in multilingual contexts and are a key facilitator of cross-lingual transfer when developing natural language processing models for low-resource languages. In…
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical…
Rank-metric codes, defined as sets of matrices over a finite field with the rank distance, have gained significant attention due to their applications in network coding and connections to diverse mathematical areas. Initially studied by…
We revisit the membership problem for subclasses of rational relations over finite and infinite words: Given a relation R in a class C_2, does R belong to a smaller class C_1? The subclasses of rational relations that we consider are formed…
This paper presents our segmentation system developed for the MLP 2017 shared tasks on cross-lingual word segmentation and morpheme segmentation. We model both word and morpheme segmentation as character-level sequence labelling tasks. The…
Folded Reed-Solomon (FRS) codes are a well-studied family of codes, known for achieving list decoding capacity. In this work, we give improved deterministic and randomized algorithms for list decoding FRS codes of rate $R$ up to radius…
Codes with local permutation constraints are described. Belief propagation decoding is shown to require the computation of permanents, and trellis-based methods for computing the permanents are introduced. New insights into the asymptotic…