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Given a partially-ordered finite alphabet $\Sigma$ and a language $L\subseteq \Sigma^*$, how large can an antichain in $L$ be (where $L$ is given the lexicographic ordering)? More precisely, since $L$ will in general be infinite, we should…

Although real-world text datasets, such as DNA sequences, are far from being uniformly random, average-case string searching algorithms perform significantly better than worst-case ones in most applications of interest. In this paper, we…

Path planning is a fundamental scientific problem in robotics and autonomous navigation, requiring the derivation of efficient routes from starting to destination points while avoiding obstacles. Traditional algorithms like A* and its…

Dictionaries are often developed using tools that save to Extensible Markup Language (XML)-based standards. These standards often allow high-level repeating elements to represent lexical entries, and utilize descendants of these repeating…

Though English sentences are typically inflexible vis-\`a-vis word order, constituents often show far more variability in ordering. One prominent theory presents the notion that constituent ordering is directly correlated with constituent…

Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths,…

Mathematical reasoning is an increasingly important indicator of large language model (LLM) capabilities, yet we lack understanding of how LLMs process even simple mathematical tasks. To address this, we reverse engineer how three mid-sized…

The approximate string matching is a fundamental and recurrent problem that arises in most computer science fields. This problem can be defined as follows: Let $D=\{x_1,x_2,\ldots x_d\}$ be a set of $d$ words defined on an alphabet…

Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…

Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…

Learning-to-rank techniques have proven to be extremely useful for prioritization problems, where we rank items in order of their estimated probabilities, and dedicate our limited resources to the top-ranked items. This work exposes a…

Reinforcement learning (RL) has become the de facto standard practice for sequential decision-making problems by improving future acting policies with feedback. However, RL algorithms may require extensive trial-and-error interactions to…

Large language models (LLMs) have significantly advanced the field of natural language processing (NLP) through their extensive parameters and comprehensive data utilization. However, existing LLMs lack a dedicated memory unit, limiting…

Large language models have achieved remarkable success on general NLP tasks, but they may fall short for domain-specific problems. Recently, various Retrieval-Augmented Large Language Models (RALLMs) are proposed to address this…

This paper focuses on extending the success of large language models (LLMs) to sequential decision making. Existing efforts either (i) re-train or finetune LLMs for decision making, or (ii) design prompts for pretrained LLMs. The former…

Large language models (LLMs) can handle a wide variety of general tasks with simple prompts, without the need for task-specific training. Multimodal Large Language Models (MLLMs), built upon LLMs, have demonstrated impressive potential in…

We introduce a new tractable temporal constraint language, which strictly contains the Ord-Horn language of Buerkert and Nebel and the class of AND/OR precedence constraints. The algorithm we present for this language decides whether a…

Combining Large Language Models (LLMs) with heuristic search algorithms like A* holds the promise of enhanced LLM reasoning and scalable inference. To accelerate training and reduce computational demands, we investigate the coreset…

A (left) quotient of a language $L$ by a word $w$ is the language $w^{-1}L=\{x\mid wx\in L\}$. The quotient complexity of a regular language $L$ is the number of quotients of $L$; it is equal to the state complexity of $L$, which is the…

We settle the equivalence between the problem of hitting a polyhedral set by the orbit of a linear map and the intersection of a regular language and a language of permutations of binary words (the permutation filter realizability problem).…