https://github.com/nathanaelsantos/convert-afnd-to-afd

https://github.com/nathanaelsantos/convert-afnd-to-afd

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• Host: GitHub
• URL: https://github.com/nathanaelsantos/convert-afnd-to-afd
• Owner: NathanaelSantos
• Created: 2020-04-26T23:58:32.000Z (over 4 years ago)
• Default Branch: master
• Last Pushed: 2024-07-19T06:55:23.000Z (6 months ago)
• Last Synced: 2024-07-19T14:59:46.273Z (6 months ago)
• Language: Java
• Size: 128 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Convert AFND to AFD

![](image/imageAFND.png)

# AFND to AFD Conversion

This project implements the conversion of a Non-deterministic Finite Automaton (AFND) to a Deterministic Finite Automaton (AFD).

## Introduction

Finite automata are used in various fields of computer science, including text processing, compiler construction, and more. A Non-deterministic Finite Automaton (AFND) allows multiple transitions for a given state and input symbol, whereas a Deterministic Finite Automaton (AFD) allows only one transition per state and input symbol. This project demonstrates the conversion process from AFND to AFD.

## Algorithm

The conversion process follows these steps:

1. **Initial State**: The initial state of the AFD is the set containing the initial state of the AFND.

2. **State Sets**: Each set of states in the AFND will be treated as a single state in the AFD.

3. **Transition Function**: For each set of states \( S \) and each symbol \( a \) in the alphabet:

   - Determine the set of states that can be reached from any state in \( S \) with the symbol \( a \), considering epsilon transitions if present.

   - This new set of states will represent a state in the AFD.

4. **Accepting States**: A state in the AFD is an accepting state if it contains at least one accepting state of the original AFND.

   

## Example

Here is an example of an AFND and its corresponding AFD:

### AFND

```

- States: {q0, q1, q2}

- Alphabet: {a, b}

- Transition function:

  - δ(q0, a) = {q0, q1}

  - δ(q0, b) = {q0}

  - δ(q1, b) = {q2}

  - δ(q2, a) = {q2}

- Initial state: q0

- Accepting states: {q2}

```

### AFD

```

- States: { {q0}, {q0, q1}, {q0, q2}, {q0, q1, q2} }

- Alphabet: {a, b}

- Transition function:

  - δ({q0}, a) = {q0, q1}

  - δ({q0}, b) = {q0}

  - δ({q0, q1}, a) = {q0, q1}

  - δ({q0, q1}, b) = {q0, q2}

  - δ({q0, q2}, a) = {q0, q2}

  - δ({q0, q2}, b) = {q0}

  - δ({q0, q1, q2}, a) = {q0, q1, q2}

  - δ({q0, q1, q2}, b) = {q0, q2}

- Initial state: {q0}

- Accepting states: { {q0, q2}, {q0, q1, q2} }

```

## Dependencies

- Java 11 or higher

- Maven 3.6 or higher