Module 5 - Discrete models

Introduction

This is a hand-in written by Group 60 (FIRE) for the weekly module #5 in the mathematical modelling course (DAT026) at Chalmers University of Technology.

Group 60 consists of:

  • Mazdak Farrokhzad

    • 901011-0279

    • twingoow@gmail.com

    • Program: IT

    • Time spent: 19 hours, 53 minutes

  • Niclas Alexandersson

    • 920203-0111

    • nicale@student.chalmers.se

    • Program: IT

    • Time spent: 27 hours, 19 minutes

We hereby declare that we have both actively participated in solving every exercise, and all solutions are entirely our own work.

Disclaimer: Please do note that the numbering of the sections in the TOC and elsewhere are not intended to follow the numbering of the problem. The problem referred to is always explicitly stated in the title itself (e.g: Problem 1...)

Problem 1 - Model types of common programs & systems

Here we briefly discuss what model types the following common programs or systems are based on.

  • A text model in a word processor can be modelled using semi structured data (SSD) such as XML. This can be done with a tree of string sequences. To process the paragraphs, sentences, and words, both the concept of regular languanges (and regular expressons for searching in the model) and the mathematical concepts that it entails can be used, as well as statistical analysis for checking if a word is particularly “non-swedish” or if a word combination is statistically improbable to have correct grammar. The statistical analysis can be done using markov chains.

  • An outliner (structured text processor) at the most basic level can be modelled using a tree of items. To each item and depending on the items type, various states can be added to it such as “enabled/disabled”, etc. More advanced implementations of outliner software that enable viewing the various states of items in a tabular format will need to be able to represent the same data in a grid.

  • The web is a series of tubes that can be modelled, assuming that it’s not the same thing as the internet and that the