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We consider the problem of sorting $n$ items, given the outcomes of $m$ pre-existing comparisons. We present a simple and natural deterministic algorithm that runs in $O(m + \log T)$ time and does $O(\log T)$ comparisons, where $T$ is the…

For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a…

Word order is an important concept in natural language, and in this work, we study how word order affects the induction of world knowledge from raw text using language models. We use word analogies to probe for such knowledge. Specifically,…

While systems designed for solving planning tasks vastly outperform Large Language Models (LLMs) in this domain, they usually discard the rich semantic information embedded within task descriptions. In contrast, LLMs possess parametrised…

Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…

Large language models (LLMs) obtain state of the art zero shot relevance ranking performance on a variety of information retrieval tasks. The two most common prompts to elicit LLM relevance judgments are pointwise scoring (a.k.a. relevance…

Large Language Models (LLMs) have shown exceptional performance in text processing. Notably, LLMs can synthesize information from large datasets and explain their decisions similarly to human reasoning through a chain of thought (CoT). An…

In this survey, we address the worst-case, average-case, and generic-case time complexity of the word problem and some other algorithmic problems in several classes of groups and show that it is often the case that the average-case…

We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We consider the case where the code-related property is…

This paper presents an approach that allows the efficient integration of speech recognition and language understanding using Tomita's generalized LR-parsing algorithm. For this purpose the GLRP-algorithm is revised so that an agenda…

Ordering the collection of states of a given automaton starting from an order of the underlying alphabet is a natural move towards a computational treatment of the language accepted by the automaton. Along this path, Wheeler \emph{graphs}…

Graph-based ranking methods, such as LexRank, are fundamental in Natural Language Processing (NLP) applications like text summarization, as they measure the relative importance of textual units. Building on recent advances in ranking…

Ranked enumeration is a query-answering paradigm where the query answers are returned incrementally in order of importance (instead of returning all answers at once). Importance is defined by a ranking function that can be specific to the…

Large language models (LLMs) have demonstrated remarkable zero-shot generalization abilities: state-of-the-art chatbots can provide plausible answers to many common questions that arise in daily life. However, so far, LLMs cannot reliably…

Reasoning language models (RLMs), also known as Large Reasoning Models (LRMs), such as OpenAI's o1 and o3, DeepSeek-R1, and Alibaba's QwQ, have redefined AI's problem-solving capabilities by extending LLMs with advanced reasoning…

We present algorithms that run in linear time on pointer machines for a collection of problems, each of which either directly or indirectly requires the evaluation of a function defined on paths in a tree. These problems previously had…

We revisit the problem of \textit{online linear optimization} in case the set of feasible actions is accessible through an approximated linear optimization oracle with a factor $\alpha$ multiplicative approximation guarantee. This setting…

In this paper we present a new parsing algorithm for linear indexed grammars (LIGs) in the same spirit as the one described in (Vijay-Shanker and Weir, 1993) for tree adjoining grammars. For a LIG $L$ and an input string $x$ of length $n$,…

Large Language Models (LLMs) still struggle with complex logical reasoning. While previous works achieve remarkable improvements, their performance is highly dependent on the correctness of translating natural language (NL) problems into a…

Optimization problems are prevalent across various scenarios. Formulating and then solving optimization problems described by natural language often requires highly specialized human expertise, which could block the widespread application…