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diff --git a/source/README.md b/source/README.md index 46afa1a..4ce2a87 100644 --- a/source/README.md +++ b/source/README.md @@ -13,6 +13,7 @@ The Working Groups are paper(s) owned by a group of persons in which they improv - WG03: `The Nectar Group`. - WG04: `The Mathematics Group`. - WG05: `The Execution Theory Group`. +- WG06: `The Debugging Group`. ## External Resources: diff --git a/source/wg06/.keep b/source/wg06/.keep new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/source/wg06/.keep diff --git a/source/wg06/articles/article.tex b/source/wg06/articles/article.tex new file mode 100644 index 0000000..9de7c82 --- /dev/null +++ b/source/wg06/articles/article.tex @@ -0,0 +1,209 @@ +%% ============================================================ +%% Academic Journal Paper Template +%% Compatible with: IEEE, ACM, Elsevier, Springer conventions +%% ============================================================ + +\documentclass[10pt, twocolumn]{article} + +%% ---- Core Packages ---------------------------------------- +\usepackage[T1]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage{lmodern} +\usepackage{microtype} % Microtypographic refinements + +%% ---- Page Geometry ---------------------------------------- +\usepackage[ + top=1in, bottom=1in, + left=0.75in, right=0.75in, + columnsep=0.25in +]{geometry} + +%% ---- Mathematics ------------------------------------------ +\usepackage{amsmath, amssymb, amsthm} +\usepackage{mathtools} +\usepackage{bm} % Bold math symbols + +%% ---- Figures & Tables ------------------------------------- +\usepackage{graphicx} +\usepackage{booktabs} % Professional table rules +\usepackage{multirow} +\usepackage{array} +\usepackage{caption} +\usepackage{subcaption} +\usepackage{float} + +%% ---- Algorithms ------------------------------------------- +\usepackage[ruled, vlined, linesnumbered]{algorithm2e} + +%% ---- Code Listings ---------------------------------------- +\usepackage{listings} +\usepackage{xcolor} + +\lstdefinestyle{codestyle}{ + backgroundcolor=\color{gray!8}, + basicstyle=\ttfamily\footnotesize, + breakatwhitespace=false, + breaklines=true, + captionpos=b, + commentstyle=\color{green!50!black}, + keywordstyle=\color{blue}\bfseries, + stringstyle=\color{orange!70!black}, + numberstyle=\tiny\color{gray}, + numbers=left, + numbersep=5pt, + showstringspaces=false, + frame=single, + rulecolor=\color{gray!40}, + tabsize=2 +} +\lstset{style=codestyle} + +%% ---- Hyperlinks ------------------------------------------- +\usepackage[ + colorlinks=true, + linkcolor=blue!70!black, + citecolor=green!50!black, + urlcolor=blue!60!black +]{hyperref} +\usepackage{url} + +%% ---- Bibliography ----------------------------------------- +\usepackage[numbers, sort&compress]{natbib} + +%% ---- Miscellaneous ---------------------------------------- +\usepackage{lipsum} % Lorem ipsum filler — remove in production +\usepackage{enumitem} +\usepackage{siunitx} % SI units: \SI{3.14}{\mega\hertz} +\usepackage{cleveref} % Smart cross-references: \cref{fig:foo} + +%% ---- Theorem Environments --------------------------------- +\theoremstyle{plain} +\newtheorem{theorem}{Theorem}[section] +\newtheorem{lemma}[theorem]{Lemma} +\newtheorem{corollary}[theorem]{Corollary} +\newtheorem{proposition}[theorem]{Proposition} + +\theoremstyle{definition} +\newtheorem{definition}[theorem]{Definition} +\newtheorem{example}[theorem]{Example} + +\theoremstyle{remark} +\newtheorem{remark}[theorem]{Remark} + +%% ---- Custom Commands -------------------------------------- +\newcommand{\R}{\mathbb{R}} +\newcommand{\N}{\mathbb{N}} +\newcommand{\Z}{\mathbb{Z}} +\newcommand{\E}{\mathbb{E}} +\newcommand{\Prob}{\mathbb{P}} +\newcommand{\norm}[1]{\left\lVert #1 \right\rVert} +\newcommand{\abs}[1]{\left\lvert #1 \right\rvert} +\newcommand{\inner}[2]{\left\langle #1,\, #2 \right\rangle} +\newcommand{\ie}{\textit{i.e.}\xspace} +\newcommand{\eg}{\textit{e.g.}\xspace} +\newcommand{\etal}{\textit{et al.}\xspace} + +%% ---- Caption Formatting ----------------------------------- +\captionsetup{ + font=small, + labelfont=bf, + format=hang, + justification=justified +} + +%% ---- Header / Footer -------------------------------------- +\usepackage{fancyhdr} +\pagestyle{fancy} +\fancyhf{} +\fancyhead[L]{\small\itshape Ne.org, Vol.~2, No.~1, March 2026} +\fancyhead[R]{\small\thepage} +\renewcommand{\headrulewidth}{0.4pt} + +%% ============================================================ +%% FRONT MATTER +%% ============================================================ + +\title{% + \vspace{-1.5em}% + \large\textbf{All you need is Integrals for Debugging.}% +} + +\author{% + \textbf{Amlal El Mahrouss}$^{1}$\thanks{Corresponding author. Email: amlal@nekernel.org} + \\amlal@nekernel.org, amlalelmahrouss@icloud.com\\[0.4em] + \small $^{1}$Ne.org Journal +} + +\date{% + \small 3 March 2026 +} + +%% ============================================================ +\begin{document} + + +\twocolumn[{% + \maketitle + \vspace{-0.5em} + \rule{\linewidth}{0.4pt} + %% ---- Abstract ------------------------------------------- + \begin{center} + \begin{minipage}{0.92\linewidth} + \small + \textbf{Abstract.}\enspace + This development presents an approach of software debugging[1] in which we'll name 'Integrals of Debuggging' (ID). + We propose a mathematical of which integrals are used to analyze, modify, and apply, software patches to programs. + + + \medskip + \textbf{Keywords:}\enspace + Computer Science; Mathematics; + \end{minipage} + \end{center} + \vspace{0.8em} + \rule{\linewidth}{0.4pt} + \vspace{1em} +}] + +\section{Introduction} + +Consider an open interval from $n$ to $p$ over a field $\mathbb{Code}$ which describes a program and its properties. What are the techniques in which we can analyze and audit its properties and behavior? We will try to impose a framework in this report. + +\section{Definition of the LongReturn(x, t) function} +\label{sec:cl-example-integrals} + +Let an integral of $\operatorname{LongReturn(x, t)}$[2] be defined where the value $n > 0$ and $p > 0, \quad n < p$: + +\begin{equation} + \operatorname{LongReturn(x, t)} \coloneqq \int_{n}^{p} \operatorname{FastReturn(x, t)} \cdot d \operatorname{t} +\end{equation} +We assume that $x$ and $t$ are always greater or equal than one, $\operatorname{LongReturn(x, t)}$ shall always be greater than $\operatorname{FastReturn(x, t)}$ for all such value in $\mathbb{Code}$. +This introduction of the LongReturn, will let us jump to our next section about its applications in Computer Analysis. + +\section{Constraints} + +However before starting, we shall provide the following conditions from [2]: +\begin{equation} + \operatorname{LongReturn(x, t)} \geq \operatorname{FastReturn(x, t)}, \quad \operatorname{x} \geq 1 +\end{equation} +The variable x shall also be defined in $\mathbb{Code}$ throughout the integral. We shall now proceed into the next section. + +\section{Definition of the DerRet(x, t) function} + +The following is the derivative of $\operatorname{LongReturn(x, t)}$, which equals to: +\begin{equation} + \operatorname{DerRet(State, Time\_State)} \coloneqq \frac{\delta \operatorname{Travel(State)}}{\delta Time\_State} + Rem +\end{equation} +Such that the following is assumed: +\begin{equation} + \quad State, \operatorname{Travel(State)} \in \mathbb{Code} +\end{equation} +Indeed, the function $\operatorname{Travel(State)}$ is equal to the program state at the variable $\operatorname{State}$ which represents the program's state. + +\section{Applications} + +One application of the $\operatorname{LongReturn(x, t)}$ is software debugging, more so, the break-point system of a debugger. The following section includes graphs to measure the efficiency of our approach in such process. + +\end{document} + + |