Related papers: Notes on Lynch-Morawska Systems
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lam\'e moduli for these…
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern…
We address the open problem of determining which classes of time-dependent linear Schr\"odinger equations and focusing and defocusing cubic and quintic non-linear Schr\"odinger equations (NLS) on unbounded domains that can be computed by an…
The unified transform method (UTM) provides a novel approach to the analysis of initial-boundary value problems for linear as well as for a particular class of nonlinear partial differential equations called integrable. If the latter…
Large Language Models (LLMs) have achieved remarkable success in various domains. However, when handling long-form text modification tasks, they still face two major problems: (1) producing undesired modifications by inappropriately…
Tools for rewriting, refactoring and optimizing code should be fast and correct. Large language models (LLMs), by their nature, possess neither of these qualities. Yet, there remains tremendous opportunity in using LLMs to improve code. We…
We present an algorithm for a class of $n$-fold ILPs: whose existing algorithms in literature typically (1) are based on the \textit{augmentation framework} where one starts with an arbitrary solution and then iteratively moves towards an…
The probabilistic method is a technique for proving combinatorial existence results by means of showing that a randomly chosen object has the desired properties with positive probability. A particularly powerful probabilistic tool is the…
There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…
We propose and analyze the perfectly matched layer (PML) method for the time-harmonic acoustic waves driven by the white noise source in the presence of the uniform flow. A PML is an artificial absorbing layer commonly used to truncate…
Large language models (LLMs) have exhibited impressive capabilities in comprehending complex instructions. However, their blind adherence to provided instructions has led to concerns regarding risks of malicious use. Existing defence…
Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…
The ability to accurately identify authorship is crucial for verifying content authenticity and mitigating misinformation. Large Language Models (LLMs) have demonstrated an exceptional capacity for reasoning and problem-solving. However,…
We present Metatheory, a comprehensive library for programming language foundations in Lean 4. The library features a modular framework for proving confluence of abstract rewriting systems using three classical proof techniques: the diamond…
Matching patients to clinical trials is a key unsolved challenge in bringing new drugs to market. Today, identifying patients who meet a trial's eligibility criteria is highly manual, taking up to 1 hour per patient. Automated screening is…
We consider the task of designing Local Computation Algorithms (LCA) for applications of the Lov\'{a}sz Local Lemma (LLL). LCA is a class of sublinear algorithms proposed by Rubinfeld et al.~\cite{Ronitt} that have received a lot of…
Much recent work has shown how cross-linguistic variation is constrained by competing pressures from efficient communication. However, little attention has been paid to the role of the systematicity of forms (regularity), a key property of…