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README.py
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# -*- coding: utf-8 -*-
# ---
# jupyter:
# jupytext:
# formats: ipynb,py:light,md
# text_representation:
# extension: .py
# format_name: light
# format_version: '1.5'
# jupytext_version: 1.11.4
# kernelspec:
# display_name: Python 3 (ipykernel)
# language: python
# name: python3
# ---
# + [markdown] tags=[]
# # Visual Automata
#
# [](https://pypi.python.org/pypi/visual-automata/)
# [](https://pypi.python.org/pypi/visual-automata/)
# [](https://pepy.tech/project/visual-automata)
# [](https://app.codecov.io/gh/lewiuberg/visual-automata)
#
# Copyright 2021 [Lewi Lie Uberg](https://uberg.me/)\
# _Released under the MIT license_
#
# Visual Automata is a Python 3 library built as a wrapper for the [Automata](https://github.com/caleb531/automata) library to add more visualization features.
#
# ## Contents
#
# - [Visual Automata](#visual-automata)
# - [Contents](#contents)
# - [Prerequisites](#prerequisites)
# - [Installing](#installing)
# - [Finite Automaton](#finite-automaton-fa)
# - [VisualDFA](#visualdfa)
# - [Importing](#importing)
# - [Instantiating DFAs](#instantiating-dfas)
# - [Converting](#converting)
# - [Transition Table](#transition-table)
# - [Minimal-DFA](#minimal-dfa)
# - [Check input strings](#check-input-strings)
# - [Show Diagram](#show-diagram)
# - [VisualNFA](#visualnfa)
# - [Importing](#importing-1)
# - [Instantiating NFAs](#instantiating-nfas)
# - [Converting](#converting-1)
# - [Transition Table](#transition-table-1)
# - [Eliminate lambda/epsilon](#eliminate-lambdaepsilon)
# - [Check input strings](#check-input-strings-1)
# - [Show Diagram](#show-diagram-1)
# - [Authors](#authors)
# - [License](#license)
# - [Acknowledgments](#acknowledgments)
#
# ## Citation
#
# ### APA
#
# ```apa
# Lie Uberg, L. (2021). Visual Automata (Version 1.1.1) [Computer software]. https://github.com/lewiuberg/visual-automata
# ```
#
# ### BibTex
#
# ```BibTex
# @misc{Lie_Uberg_Visual_Automata_2021,
# author = {Lie Uberg, Lewi},
# month = {4},
# title = {{Visual Automata}},
# url = {https://github.com/lewiuberg/visual-automata},
# year = {2021}
# }
# ```
#
# hub.com/pandas-dev/pandas)\
# [`pip install graphviz`](https://github.com/xflr6/graphviz)\
# [`pip install colormath`](https://github.com/gtaylor/python-colormath)\
# [`pip install jupyterlab`](https://github.com/jupyterlab/jupyterlab)
#
# ## Installing
#
# [`pip install visual-automata`](https://pypi.org/project/visual-automata/)
#
# ## Finite Automaton (FA)
#
# ### VisualDFA
#
# #### Importing
#
# Import needed classes.
# +
from automata.fa.dfa import DFA
from visual_automata.fa.dfa import VisualDFA
# -
# #### Instantiating DFAs
#
# Define an visual_automata DFA that can accept any string ending with 00 or 11.
dfa = VisualDFA(
states={"q0", "q1", "q2", "q3", "q4"},
input_symbols={"0", "1"},
transitions={
"q0": {"0": "q3", "1": "q1"},
"q1": {"0": "q3", "1": "q2"},
"q2": {"0": "q3", "1": "q2"},
"q3": {"0": "q4", "1": "q1"},
"q4": {"0": "q4", "1": "q1"},
},
initial_state="q0",
final_states={"q2", "q4"},
)
# #### Converting
#
# An automata-lib DFA can be converted to a VisualDFA.
#
# Define an automata-lib DFA that can accept any string ending with 00 or 11.
dfa = DFA(
states={"q0", "q1", "q2", "q3", "q4"},
input_symbols={"0", "1"},
transitions={
"q0": {"0": "q3", "1": "q1"},
"q1": {"0": "q3", "1": "q2"},
"q2": {"0": "q3", "1": "q2"},
"q3": {"0": "q4", "1": "q1"},
"q4": {"0": "q4", "1": "q1"},
},
initial_state="q0",
final_states={"q2", "q4"},
)
# Convert automata-lib DFA to VisualDFA.
dfa = VisualDFA(dfa)
# #### Transition Table
#
# Outputs the transition table for the given DFA.
dfa.table
# ```text
# 0 1
# →q0 q3 q1
# q1 q3 *q2
# *q2 q3 *q2
# q3 *q4 q1
# *q4 *q4 q1
# ```
#
# #### Minimal-DFA
#
# Creates a minimal DFA which accepts the same inputs as the old one. Unreachable states are removed and equivalent states are merged. States are renamed by default.
new_dfa = VisualDFA(
states={'q0', 'q1', 'q2'},
input_symbols={'0', '1'},
transitions={
'q0': {'0': 'q0', '1': 'q1'},
'q1': {'0': 'q0', '1': 'q2'},
'q2': {'0': 'q2', '1': 'q1'}
},
initial_state='q0',
final_states={'q1'}
)
new_dfa.table
# ```text
# 0 1
# →q0 q0 *q1
# *q1 q0 q2
# q2 q2 *q1
# ```
new_dfa.show_diagram()
# 
minimal_dfa = VisualDFA.minify(new_dfa)
minimal_dfa.show_diagram()
# 
minimal_dfa.table
# ```text
# 0 1
# →{q0,q2} {q0,q2} *q1
# *q1 {q0,q2} {q0,q2}
# ```
#
# #### Check input strings
#
# `1001` does not end with `00` or `11`, and is therefore `Rejected`
dfa.input_check("1001")
# ```text
# [Rejected]
# Step: Current state: Input symbol: New state:
# 1 →q0 1 q1
# 2 q1 0 q3
# 3 q3 0 *q4
# 4 *q4 1 q1
# ```
#
# `10011` does end with `11`, and is therefore `Accepted`
dfa.input_check("10011")
# ```text
# [Accepted]
# Step: Current state: Input symbol: New state:
# 1 →q0 1 q1
# 2 q1 0 q3
# 3 q3 0 *q4
# 4 *q4 1 q1
# 5 q1 1 *q2
# ```
#
# #### Show Diagram
#
# For IPython `dfa.show_diagram()` may be used.\
# For a python script `dfa.show_diagram(view=True)` may be used to automatically view the graph as a PDF file.
dfa.show_diagram()
# 
#
# The `show_diagram` method also accepts input strings, and will return a graph with gradient `red` arrows for `Rejected` results, and gradient `green` arrows for `Accepted` results. It will also display a table with transitions states stepwise. The steps in this table will correspond with the `[number]` over each traversed arrow.
#
# Please note that for visual purposes additional arrows are added if a transition is traversed more than once.
dfa.show_diagram("1001")
# ```text
# [Rejected]
# Step: Current state: Input symbol: New state:
# 1 →q0 1 q1
# 2 q1 0 q3
# 3 q3 0 *q4
# 4 *q4 1 q1
# ```
#
# 
dfa.show_diagram("10011")
# ```text
# [Accepted]
# Step: Current state: Input symbol: New state:
# 1 →q0 1 q1
# 2 q1 0 q3
# 3 q3 0 *q4
# 4 *q4 1 q1
# 5 q1 1 *q2
# ```
#
# 
#
# ### VisualNFA
#
# #### Importing
#
# Import needed classes.
# +
from automata.fa.nfa import NFA
from visual_automata.fa.nfa import VisualNFA
# -
# #### Instantiating NFAs
#
# Define an visual_automata NFA that can accept any string with the pattern 10, 1010, 101010.
nfa = VisualNFA(
states={"q0", "q1", "q2"},
input_symbols={"0", "1"},
transitions={
"q0": {"": {"q2"}, "1": {"q1"}},
"q1": {"1": {"q2"}, "0": {"q0", "q2"}},
"q2": {},
},
initial_state="q0",
final_states={"q0"},
)
# #### Converting
#
# An automata-lib NFA can be converted to a VisualNFA.
#
# Define an automata-lib NFA that can accept any string with the pattern 10, 1010, 101010.
nfa = NFA(
states={"q0", "q1", "q2"},
input_symbols={"0", "1"},
transitions={
"q0": {"": {"q2"}, "1": {"q1"}},
"q1": {"1": {"q2"}, "0": {"q0", "q2"}},
"q2": {},
},
initial_state="q0",
final_states={"q0"},
)
# Convert automata-lib NFA to VisualNFA.
nfa = VisualNFA(nfa)
# #### Transition Table
#
# Outputs the transition table for the given DFA.
nfa.table
# ```text
# 0 1 λ
# →*q0 ∅ q1 q2
# q1 {*q0,q2} q2 ∅
# q2 ∅ ∅ ∅
# ```
#
# #### Eliminate lambda/epsilon
#
# Creates a NFA with lambda transitions removed.
nfa_eliminated = VisualNFA.eliminate_lambda(nfa)
nfa_eliminated.table
# ```text
# 0 1
# →*q0 ∅ q1
# q1 {*q0,q2} q2
# q2 ∅ ∅
# ```
nfa_eliminated.show_diagram()
# 
#
# #### Check input strings
#
# `101` does not correspond with the pattern `10`, `1010`, `101010`, and is therefore `Rejected`
nfa.input_check("101")
# ```text
# [Rejected]
# Step: Current state: Input symbol: New state:
# 1 →*q0 1 q1
# 2 q1 0 q2
# 3 q2 1 ∅
# ```
#
# `1010` does correspond with the pattern `10`, `1010`, `101010`, and is therefore `Accepted`
nfa.input_check("1010")
# ```text
# [Accepted]
# Step: Current state: Input symbol: New state:
# 1 →*q0 1 q1
# 2 q1 0 →*q0
# 3 →*q0 1 q1
# 4 q1 0 →*q0
# ```
#
# #### Show Diagram
#
# For IPython `nfa.show_diagram()` may be used.\
# For a python script `nfa.show_diagram(view=True)` may be used to automatically view the graph as a PDF file.
nfa.show_diagram()
# 
#
# The `show_diagram` method also accepts input strings, and will return a graph with gradient `red` arrows for `Rejected` results, and gradient `green` arrows for `Accepted` results. It will also display a table with transitions states stepwise. The steps in this table will correspond with the `[number]` over each traversed arrow.
#
# Please note that for visual purposes additional arrows are added if a transition is traversed more than once.
nfa.show_diagram("101")
# ```text
# [Rejected]
# Step: Current state: Input symbol: New state:
# 1 →*q0 1 q1
# 2 q1 0 q2
# 3 q2 1 ∅
# ```
#
# 
nfa.show_diagram("1010")
# ```text
# [Accepted]
# Step: Current state: Input symbol: New state:
# 1 →*q0 1 q1
# 2 q1 0 →*q0
# 3 →*q0 1 q1
# 4 q1 0 →*q0
# ```
#
# 
#
# Please note that for long input strings, the path calculations may take some time.
big_nfa = VisualNFA(
states={"q1", "q2", "q3", "q4", "q5", "q6", "q7", "q8"},
input_symbols={"A", "C", "G", "T"},
transitions={
"q1": {"A": {"q7"}, "C": {"q4"}, "G": {"q4", "q2"}, "T": {"q4"}},
"q2": {"A": {"q3", "q6"}, "C": {"q2", "q4"}, "G": {"q3", "q6"}, "T": {"q6"}},
"q3": {"A": {"q8"}, "C": {"q8"}, "T": {"q8"}},
"q4": {"A": {"q5"}, "C": {"q4"}, "G": {"q5"}, "T": {"q2", "q4", "q5"}},
"q5": {"A": {"q3", "q8"}, "C": {"q3", "q8"}, "G": {"q8"}, "T": {"q3", "q8"}},
"q6": {"A": {"q8"}, "C": {"q8"}, "G": {"q8"}, "T": {"q8"}},
"q7": {"A": {"q7", "q8"}, "C": {"q7", "q8"}, "G": {"q8"}, "T": {"q3", "q8"}},
"q8": {},
},
initial_state="q1",
final_states={"q8"},
)
big_nfa.table
big_nfa.show_diagram("CGC")
# ```text
# [Accepted]
# Step: Current state: Input symbol: New state:
# 1 →q1 C q4
# 2 q4 G q5
# 3 q5 C *q8
# ```
#
# 
#
# ## Authors
#
# - **[Lewi Lie Uberg](https://github.com/lewiuberg)** - [uberg.me](https://uberg.me/)
#
# ## License
#
# This project is licensed under the MIT License - see the [LICENSE.md](https://github.com/lewiuberg/visual-automata/blob/master/LICENSE.txt) file for details
#
# ## Acknowledgments
#
# - [Caleb Evans](https://github.com/caleb531) for his work on automata-lib.
# - [Geir Arne Hjelle](https://github.com/gahjelle), [Michal Porteš](https://github.com/mportesdev), and [Bart Willems](https://github.com/bart-r-willems) for their general counsel.
# - [Dr. Seifedine Kadry](https://www.noroff.no/en/contact/staff/53-academic/423-seifedine-kadry). My _Further Discrete Mathematics_ professor at **Noroff University College**, for teaching me Automata.
# - [JFLAP](http://www.jflap.org) for their work on a GUI based Automata application.