Visual Automata is a Python 3 library built as a wrapper for Caleb Evans' Automata library to add more visualization features.

Overview

Latest Version Supported Python versions Downloads

Visual Automata

Copyright 2021 Lewi Lie Uberg
Released under the MIT license

Visual Automata is a Python 3 library built as a wrapper for Caleb Evans' Automata library to add more visualization features.

Contents

Prerequisites

pip install automata-lib
pip install pandas
pip install graphviz
pip install colormath
pip install jupyterlab

Installing

pip install visual-automata

VisualDFA

Importing

Import needed classes.

from automata.fa.dfa import DFA

from visual_automata.fa.dfa import VisualDFA

Instantiating DFAs

Define an automata-lib 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)

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
      0    1
→q0  q0  *q1
*q1  q0   q2
q2   q2  *q1
new_dfa.show_diagram()

alt text

minimal_dfa = VisualDFA.minify(new_dfa)
minimal_dfa.show_diagram()

alt text

minimal_dfa.table
                0        1
→{q0,q2}  {q0,q2}      *q1
*q1       {q0,q2}  {q0,q2}

Transition Table

Outputs the transition table for the given DFA.

dfa.table
       0    1
→q0   q3   q1
q1    q3  *q2
*q2   q3  *q2
q3   *q4   q1
*q4  *q4   q1

Check input strings

1001 does not end with 00 or 11, and is therefore Rejected

dfa.input_check("1001")
          [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")
          [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()

alt text

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")
          [Rejected]                         
Step: Current state: Input symbol: New state:
1                →q0             1         q1
2                 q1             0         q3
3                 q3             0        *q4
4                *q4             1         q1

alt text

dfa.show_diagram("10011")
          [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

alt text

Authors

License

This project is licensed under the MIT License - see the LICENSE.md file for details

Acknowledgments

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Comments
  • FrozenNFA constructor attempts to call deepcopy on frozendicts

    FrozenNFA constructor attempts to call deepcopy on frozendicts

    The VisualNFA constructor attempts to create a deep copy of the passed nfa, especially the transitions dictionary: https://github.com/lewiuberg/visual-automata/blob/3ea0cdc4de9d3919250919b70fbc036d75120a85/visual_automata/fa/nfa.py#L469

    The deepcopy method is monkeypatched onto dict via curse: https://github.com/lewiuberg/visual-automata/blob/3ea0cdc4de9d3919250919b70fbc036d75120a85/visual_automata/fa/nfa.py#L32

    However, automata-lib 7.0.1 returns a frozendict from the frozendict package instead, so the method call fails. It is not clear if copying the frozendict is at all necessary; deepcopy returns the object as-is.

    MRE

    Using most recent versions:

    • automata-lib 7.0.1
    • visual_automata 1.1.1
    from automata.fa.nfa import NFA
    from visual_automata.fa.nfa import VisualNFA
    
    nfa = NFA(states={"q0"}, input_symbols={"i0"}, transitions={"q0": {"i0": {"q0"}}}, initial_state="q0",
              final_states={"q0"})
    VisualNFA(nfa).show_diagram(view=True)
    

    Expected Behavior

    The automaton is shown.

    Actual Behavior

    Traceback (most recent call last):
      File "/path/to/scratch_1.py", line 6, in <module>
        VisualNFA(nfa).show_diagram(view=True)
      File "/path/to/site-packages/visual_automata/fa/nfa.py", line 619, in show_diagram
        all_transitions_pairs = self._transitions_pairs(self.nfa.transitions)
      File "/path/to/site-packages/visual_automata/fa/nfa.py", line 469, in _transitions_pairs
        all_transitions = all_transitions.deepcopy()
    AttributeError: 'frozendict.frozendict' object has no attribute 'deepcopy'
    
    opened by no-preserve-root 3
  • VisualDFA constructor implicitly checks wrapped automaton cardinality

    VisualDFA constructor implicitly checks wrapped automaton cardinality

    The VisualDFA constructor checks the dfa parameter using https://github.com/lewiuberg/visual-automata/blob/3ea0cdc4de9d3919250919b70fbc036d75120a85/visual_automata/fa/dfa.py#L34

    This checks if dfa is truthy. Since the DFA class defines a __len__ method (and no __bool__), is is truthy iff len(dfa) != 0. Unfortunately, the length checks the dfa's cardinality, i.e., the size if the input language. For infinite-language DFAs, an exception is then raised. As a result, infinite DFAs cannot be visualized.

    This could be fixed by testing if dfa is None. VisualNFA is not affected since NFA does not define a __len__ method at the moment, but would fail if a similar method would be added to NFA.

    MRE

    Using most recent versions:

    • automata-lib 7.0.1
    • visual_automata 1.1.1
    from automata.fa.dfa import DFA
    from visual_automata.fa.dfa import VisualDFA
    
    dfa = DFA(states={"q0"}, input_symbols={"i0"}, transitions={"q0": {"i0": "q0"}}, initial_state="q0",
              final_states={"q0"})
    VisualDFA(dfa).show_diagram(view=True)
    

    Expected Behavior

    The automaton is shown.

    Actual Behavior

    Traceback (most recent call last):
      File "/path/to/scratch_1.py", line 6, in <module>
        VisualDFA(dfa).show_diagram(view=True)
      File "/path/to/site-packages/visual_automata/fa/dfa.py", line 34, in __init__
        if dfa:
      File "/path/to/site-packages/automata/fa/dfa.py", line 160, in __len__
        return self.cardinality()
      File "/path/to/site-packages/automata/fa/dfa.py", line 792, in cardinality
        raise exceptions.InfiniteLanguageException("The language represented by the DFA is infinite.")
    automata.base.exceptions.InfiniteLanguageException: The language represented by the DFA is infinite.
    

    Workaround

    Manually copying the automaton works:

    VisualDFA(states=dfa.states, input_symbols=dfa.input_symbols, transitions=dfa.transitions,
              initial_state=dfa.initial_state, final_states=dfa.final_states).show_diagram(view=True)
    
    opened by no-preserve-root 1
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