Related papers: On Minimal Pumping Constants for Regular Languages
Set theory is foundational to mathematics and, when sets are finite, to reasoning about the world. An intelligent system should perform set operations consistently, regardless of superficial variations in the operands. Initially designed…
In this paper, we examine regularity issues for two damped abstract elastic systems; the damping and coupling involve fractional powers $\mu, \theta$, with $0 \leq \mu , \theta \leq 1$, of the principal operators. The matrix defining the…
Recent advancements in large language models (LLMs) have shown promise in multi-step reasoning tasks, yet their reliance on extensive manual labeling to provide procedural feedback remains a significant impediment. To address this…
This paper considers the minimization of a continuously differentiable function over a cardinality constraint. We focus on smooth and relatively smooth functions. These smoothness criteria result in new descent lemmas. Based on the new…
Given a regular language $L$, we study the language of words $\mathsf{D}(L)$, that distinguish between pairs of different left-quotients of $L$. We characterize this distinguishability operation, show that its iteration has always a fixed…
We study the state complexity of regular operations in the class of ideal languages. A language L over an alphabet Sigma is a right (left) ideal if it satisfies L = L Sigma* (L = Sigma* L). It is a two-sided ideal if L = Sigma* L Sigma *,…
We present methods to compute least fixed points of multiple monotone inflationary functions in parallel and distributed settings. While the classic Knaster-Tarski theorem addresses a single function with sequential iteration, modern…
Fine-tuned pre-trained language models (PLMs) have achieved awesome performance on almost all NLP tasks. By using additional prompts to fine-tune PLMs, we can further stimulate the rich knowledge distributed in PLMs to better serve…
In this paper we explore where information is collected and how it is propagated throughout layers in large language models (LLMs). We begin by examining the surprising computational importance of punctuation tokens which previous work has…
We present a new characteristic of a regular ideal language called reset complexity. We find some bounds on the reset complexity in terms of the state complexity of a given language. We also compare the reset complexity and the state…
In this report we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic Buchi, Co-Buchi, and parity…
Recent advances in large pre-trained language models (PLMs) lead to impressive gains in natural language understanding (NLU) tasks with task-specific fine-tuning. However, directly fine-tuning PLMs heavily relies on sufficient labeled…
(Rephrased) Non-conformance decision-making processes in high-precision manufacturing of engineering structures are often delayed due to numerical simulations that are needed for analyzing the defective parts and assemblies. Interfaces…
The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of…
We study the permutation complexity of finite-state stationary stochastic processes based on a duality between values and orderings between values. First, we establish a duality between the set of all words of a fixed length and the set of…
The large language models have achieved superior performance on various natural language tasks. One major drawback of such approaches is they are resource-intensive in fine-tuning new datasets. Soft-prompt tuning presents a…
Lemmatization of standard languages is concerned with (i) abstracting over morphological differences and (ii) resolving token-lemma ambiguities of inflected words in order to map them to a dictionary headword. In the present paper we aim to…
The reasoning ability of large language models (LLMs) has been rapidly advancing in recent years, attracting interest in more fundamental approaches that can reliably enhance their generalizability. This work demonstrates that model…
This thesis deals with the specification and construction of syntax and operational semantics of a programming language. We work with a general notion of signature for specifying objects of a given category as initial objects in a suitable…
These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these…