Related papers: Coding over Core Models
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
Recently, there has been increasing activity in using deep learning for software engineering, including tasks like code generation and summarization. In particular, the most recent coding Large Language Models seem to perform well on these…
Large language models (LLMs) and transformer-based architectures are increasingly utilized for source code analysis. As software systems grow in complexity, integrating LLMs into code analysis workflows becomes essential for enhancing…
The study of inner models was initiated by G\"odel's analysis of the constructible universe. Later, the study of canonical inner models with large cardinals, e.g., measurable cardinals, strong cardinals or Woodin cardinals, was pioneered by…
Large Language Models (LLMs) have garnered remarkable advancements across diverse code-related tasks, known as Code LLMs, particularly in code generation that generates source code with LLM from natural language descriptions. This…
We describe a Martin-L\"of style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
From pre-trained language model (PLM) to large language model (LLM), the field of natural language processing (NLP) has witnessed steep performance gains and wide practical uses. The evaluation of a research field guides its direction of…
This paper is an expanded version of two talks given by the author at the Summer School on the Interactions between Homotopy Theory and Algebra at the University of Chicago, July 26 to August 6, 2004. It describes a connection between model…
Inspired by Zermelo's quasi-categoricity result characterizing the models of second-order Zermelo-Fraenkel set theory $\text{ZFC}_2$, we investigate when those models are fully categorical, characterized by the addition to $\text{ZFC}_2$…
A coding problem for correlated information sources is investigated. Messages emitted from two correlated sources are jointly encoded, and delivered to two decoders. Each decoder has access to one of the two messages to enable it to…
In this survey article (which hitherto is an ongoing work-in-progress) we present the formulation of the induction and coinduction principles using the language and conventions of each of order theory, set theory, programming languages'…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
This paper investigates properties of polar codes that can be potentially useful in real-world applications. We start with analyzing the performance of finite-length polar codes over the binary erasure channel (BEC), while assuming belief…
Understanding source code is a topic of great interest in the software engineering community, since it can help programmers in various tasks such as software maintenance and reuse. Recent advances in large language models (LLMs) have…
The existence of $q$-ary linear complementary pairs (LCPs) of codes with $q> 2$ has been completely characterized so far. This paper gives a characterization for the existence of binary LCPs of codes. As a result, we solve an open problem…
Code large language models mark a pivotal breakthrough in artificial intelligence. They are specifically crafted to understand and generate programming languages, significantly boosting the efficiency of coding development workflows. In…
A main theme of the paper is a conjecture of Bloch-Kato on the image of $p$-adic regulator maps for a proper smooth variety $X$ over an algebraic number field $k$. The conjecture for a regulator map of particular degree and weight is…
We apply the theory of superselection sectors in the same way as done by G.Mack and V.Schomerus for the Ising model to generalizations of this model described by J.Fr\"{o}hlich and T.Kerler.
Proving capacity for networks without feedback or cooperation usually involves two fundamental random coding techniques: superposition coding and binning. Although conceptually very different, these two techniques often achieve the same…
Two major areas of interest in the era of Large Language Models regard questions of what do LLMs know, and if and how they may be able to reason (or rather, approximately reason). Since to date these lines of work progressed largely in…