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We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
We consider deletion correcting codes over a q-ary alphabet. It is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions. To obtain asymptotic upper bounds on code…
We develop invariants of the lower central series of free groups through linking of letters, showing they span the rational linear dual of the lower central series subquotients. We build on an approach to Lie coalgebras through operads,…
Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs during real-life construction made it impractical for truly massive datasets such as…
We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence which only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic…
A text written using symbols from a given alphabet can be compressed using the Huffman code, which minimizes the length of the encoded text. It is necessary, however, to employ a text-specific codebook, i.e. the symbol-codeword dictionary,…
We propose Seq2Edits, an open-vocabulary approach to sequence editing for natural language processing (NLP) tasks with a high degree of overlap between input and output texts. In this approach, each sequence-to-sequence transduction is…
Language models have proven successful across a wide range of software engineering tasks, but their significant computational costs often hinder their practical adoption. To address this challenge, researchers have begun applying various…
Morphologically rich languages accentuate two properties of distributional vector space models: 1) the difficulty of inducing accurate representations for low-frequency word forms; and 2) insensitivity to distinct lexical relations that…
Transformer models have achieved state-of-the-art results in a wide range of NLP tasks including summarization. Training and inference using large transformer models can be computationally expensive. Previous work has focused on one…
The small $x$ behavior of the flavor non-singlet $g_{1}$ structure function is analysed numerically by taking into account the all-order resummation of $\alpha_{s} \ln^{2}x $ terms. We include a part of the next-to-leading logarithmic…
In this note, we establish the convexity and monotonicity for affine standard Lyndon words in all types, generalizing the $A$-type results of arXiv:2305.16299. We also derive partial results on the structure of imaginary standard Lyndon…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
We propose a generalized version of context-sensitivity in term rewriting based on the notion of "forbidden patterns". The basic idea is that a rewrite step should be forbidden if the redex to be contracted has a certain shape and appears…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
Through reading the documentation in the context, tool-using language models can dynamically extend their capability using external tools. The cost is that we have to input lengthy documentation every time the model needs to use the tool,…
The state complexity of the result of a regular operation is often positively correlated with the number of distinct transformations induced by letters in the minimal deterministic finite automaton of the input languages. That is, more…
Order diagrams allow human analysts to understand and analyze structural properties of ordered data. While an experienced expert can create easily readable order diagrams, the automatic generation of those remains a hard task. In this work,…
Authorship analysis is an important subject in the field of natural language processing. It allows the detection of the most likely writer of articles, news, books, or messages. This technique has multiple uses in tasks related to…
In machine translation, rare words continue to be a problem for the dominant encoder-decoder architecture, especially in low-resource and out-of-domain translation settings. Human translators solve this problem with monolingual or bilingual…