Related papers: Linear Programming Bounds
This document is an informal bibliography of the papers dealing with distributed approximation algorithms. A classic setting for such algorithms is bounded degree graphs, but there is a whole set of techniques that have been developed for…
Understanding code represents a core ability needed for automating software development tasks. While foundation models like LLMs show impressive results across many software engineering challenges, the extent of their true semantic…
In this work, we explore explicit Large Language Model (LLM)-powered support for the iterative design of computer programs. Program design, like other design activity, is characterized by navigating a space of alternative problem…
The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where…
Binary code analysis plays a pivotal role in the field of software security and is widely used in tasks such as software maintenance, malware detection, software vulnerability discovery, patch analysis, etc. However, unlike source code,…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings,…
In the setting of minimal local grammar-based coding, the input string is represented as a grammar with the minimal output length defined via simple symbol-by-symbol encoding. This paper discusses four contributions to this field. First, we…
I'll outline the latest version of my limits of math course. The purpose of this course is to illustrate the proofs of the key information-theoretic incompleteness theorems of algorithmic information theory by means of algorithms written in…
The latest in a series of reports presenting the information-theoretic incompleteness theorems of algorithmic information theory via algorithms written in specially designed versions of LISP. Previously in this LISP code only one-character…
In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…
In this paper we present an extension of known semidefinite and linear programming upper bounds for spherical codes and consider a version of this bound for distance graphs. We apply the main result for the distance distribution of a…
Future wireless applications such as high definition video streaming, wireless cloud radio access networks, and cellular data offload are bandwidth-hungry, which highlights the need for Wi-Fi links exceeding 1 Gb/s. This article discusses…
We study the minimum number of minimal codewords in linear codes from the point of view of projective geometry. We derive bounds and in some cases determine the exact values. We also present an extension to minimal subcode supports.
Language modeling studies the probability distributions over strings of texts. It is one of the most fundamental tasks in natural language processing (NLP). It has been widely used in text generation, speech recognition, machine…
Slicing is a program analysis technique originally developed for imperative languages. It facilitates understanding of data flow and debugging. This paper discusses slicing of Constraint Logic Programs. Constraint Logic Programming (CLP) is…
Large language models (LLMs) are being increasingly adopted for programming work. Prior work shows that while LLMs accelerate task completion for professional programmers, beginning programmers struggle to prompt models effectively.…
Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5)…
Retrograde analysis reads programs from the end to the beginning: treat statements as constraints on prior states, propagate sets of states backward, and compare the reachable inputs with the intended specification. This tutorial condenses…
We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same…