Related papers: Optimal LZ-End Parsing is Hard

We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its reversal. We call this problem…

We introduce the problem of computing a parsing where each phrase is of length at most $m$ and which minimizes the zeroth order entropy of parsing. Based on the recent theoretical results we devise a heuristic for this problem. The solution…

Some airlines use the preferential bidding system to construct the schedules of their pilots. In this system, the pilots bid on the different activities and the schedules that lexicographically maximize the scores of the pilots according to…

We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…

Finite valued constraint satisfaction problems are a formalism for describing many natural optimization problems, where constraints on the values that variables can take come with rational weights and the aim is to find an assignment of…

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Generating semantically coherent text requires a robust internal representation of linguistic structures, which traditional embedding techniques often fail to capture adequately. A novel approach, Latent Lexical Projection (LLP), is…

In contrast to the advances in characterizing the sample complexity for solving Markov decision processes (MDPs), the optimal statistical complexity for solving constrained MDPs (CMDPs) remains unknown. We resolve this question by providing…

We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…

Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit…

Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…

Vizing's theorem guarantees that every graph with maximum degree $\Delta$ admits an edge coloring using $\Delta + 1$ colors. In online settings - where edges arrive one at a time and must be colored immediately - a simple greedy algorithm…

We study the recursion-theoretic complexity of Positive Almost-Sure Termination ($\mathsf{PAST}$) in an imperative programming language with rational variables, bounded nondeterministic choice, and discrete probabilistic choice. A program…

Vision-language models (VLMs) transform environment percepts into vision-language semantics interpretable by LLMs. However, completing complex tasks often requires reasoning about information beyond what is currently perceived. We propose…

We study the complexity of approximating solution structure of the bijective weighted sentence alignment problem of DeNero and Klein (2008). In particular, we consider the complexity of finding an alignment that has a significant overlap…

Word alignment was once a core unsupervised learning task in natural language processing because of its essential role in training statistical machine translation (MT) models. Although unnecessary for training neural MT models, word…

We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in $O(N\log N)$ time and uses only $O(N\log\sigma)$ bits of working space, where $N$ is the length of the string and $\sigma$ is the size of…

We present a new algorithm for computing the Lempel-Ziv Factorization (LZ77) of a given string of length $N$ in linear time, that utilizes only $N\log N + O(1)$ bits of working space, i.e., a single integer array, for constant size integer…

Prior methods to text segmentation are mostly at token level. Despite the adequacy, this nature limits their full potential to capture the long-term dependencies among segments. In this work, we propose a novel framework that incrementally…

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…