Related papers: Coding over Core Models
Living organisms are the most complex, interesting and significant objects regarding all substructures of the universe. Life science is regarded as a science of the 21st century and one can expect great new discoveries in the near futures.…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
Generalising slightly the notions of a strict computability model and of a simulation between them, which were elaborated by Longley and Normann, we define canonical computability models over categories and appropriate Set-valued functors…
Computation codes in network information theory are designed for the scenarios where the decoder is not interested in recovering the information sources themselves, but only a function thereof. K\"orner and Marton showed for distributed…
Large language models (LLMs) have brought a paradigm shift to the field of code generation, offering the potential to enhance the software development process. However, previous research mainly focuses on the accuracy of code generation,…
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…
We study the problem of building generative models of natural source code (NSC); that is, source code written and understood by humans. Our primary contribution is to describe a family of generative models for NSC that have three key…
In this paper, a construction of $(n,k,\delta)$ LDPC convolutional codes over arbitrary finite fields, which generalizes the work of Robinson and Bernstein and the later work of Tong is provided. The sets of integers forming a…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
Large Language Models (LLMs) have demonstrated notable proficiency in both code generation and comprehension across multiple programming languages. However, the mechanisms underlying this proficiency remain underexplored, particularly with…
Our main result is elementary and concerns the relationship between the multiplicative groups of the coordinate and endomorphism rings of the formal additive group over a field of characteristic $p>0$. The proof involves the combinatorics…
In this paper, based on the contributions of Tucker (1983) and Seb{\H{o}} (1992), we generalize the concept of a sequential coloring of a graph to a framework in which the algorithm may use a coloring rule-base obtained from suitable…
The article provides a survey on convolutional codes stressing the connections to module theory and systems theory. Constructions of codes with maximal possible distance and distance profile are provided. The article will appear as book…
Deep Learning (DL) techniques for Natural Language Processing have been evolving remarkably fast. Recently, the DL advances in language modeling, machine translation and paragraph understanding are so prominent that the potential of DL in…
We provide a construction which covers as special cases many of the topologies on integers one can find in the literature. Moreover, our analysis of the Golomb and Kirch topologies inserts them in a family of connected, Hausdorff topologies…
We introduce a path-theoretic framework for understanding the representation theory of (quantum) symmetric and general linear groups and their higher level generalisations over fields of arbitrary characteristic. Our first main result is a…
A generalized theory of spatial coherence for superposition of two speckle patterns with polarization diversity is presented. The presented theory deals with superposition in different scenarios i.e. superposition of two fully correlated,…
Turing's famous 'machine' model constitutes the first intuitively convincing framework for computing with real numbers. Kleene's computation schemes S1-S9 extend Turing's approach and provide a framework for computing with objects of any…
The field of computability and complexity was, where computer science sprung from. Turing, Church, and Kleene all developed formalisms that demonstrated what they held "intuitively computable". The times change however and today's…
Code generation is a longstanding challenge, aiming to generate a code snippet based on a natural language description. Usually, expensive text-code paired data is essential for training a code generation model. Recently, thanks to the…