thienanh96 / automata-operations-on-relations

Implementations of operations on relations - An algorithmic approach , Automata theory.

Automata-Operations-on-relations

Operations on Relations: Implementations

Modeling with Automata , Hanoi University of Science and Technology
Group 1:

• Pham Van Tien
• Nguyen Thien Anh
• Vu Nhat Anh

Introduction

Automata-Operations-on-relations is a project written in Javascript , using Nodejs which is a JavaScript runtime. Based on Chapter 6 of the lecture notes: Automata theory , an algorithmic approach - Javier Esparza released on August 26 , 2017 , this project is constructed, concentrating on implementing some algorithms of operations on relations. We implemented 5 operations : PROJECT ( on component 1 ) , PROJECT ( on component 2 ) , JOIN , POST, PRE. We also implemented the NFA-to-DFA conversion , state minimization ( remove unreachable states , merge equivalent states ) to reduce the number of states.
In term of this project, we used examples in that above lecture notes to conveniently help you follow.

Installation

1. Download and install Nodejs.
2. Download this project and extract the zip file.

Usage

1. The .jff input files are in input folder, they are examples so you can replace them by others.
2. Go into project folder by command line , then type npm install xml2js to create node modules folder and download xml2js library
3. Go into project folder by command line , then type node buildxml
4. The .jff output files will be created in output folder , they will be opened automatically with JFlap.

About algorithms

Projection operation

Join operation

Post operation

We only have to replace lines 7-8 of join's algorithm by this two line to get post's algorithm

Pre operation

We only have to replace lines 7-8 of join's algorithm by this two line to get post's algorithm

Pad closure function

State minimization

1. Convert NFA to DFA
   First we need to do this before implementing the state minimization.
   Refer to this link for the algorithm.
2. Remove unreachable states
   First, we need to identify the reachable states
   
   Eventually, we remove the unreachable states
3. Merge the equivalent states