Pure-Python library for building and working with nondeterministic finite automata (NFAs).
This library makes it possible to concisely construct nondeterministic finite automata (NFAs) using common Python data structures and operators, as well as to perform common operations involving NFAs. NFAs are represented using a class derived from the Python dictionary type, wherein dictionary objects serve as individual states and dictionary entries serve as transitions (with dictionary keys representing transition labels).
This library is available as a package on PyPI:
python -m pip install nfa
The library can be imported in the usual way:
import nfa from nfa import nfa
This library makes it possible to concisely construct an NFA by using one or more instances of the nfa class. In the example below, an NFA is defined in which transition labels are strings:
>>> from nfa import nfa
>>> n = nfa({'a': nfa({'b': nfa({'c': nfa()})})})
The nfa object can be applied to a sequence of symbols (represented as an iterable of transition labels). This returns the length (as an integer) of the longest path that (1) traverses an ordered sequence of the NFA's transitions whose labels match the sequence of symbols supplied as the argument and (2) terminates at an accepting state:
>>> n(['a', 'b', 'c']) 3
By default, an empty NFA object nfa() is an accepting state and a non-empty object is not an accepting state. When an NFA is applied to an iterable of labels that does not traverse a path that leads to an accepting state, None is returned:
>>> n(['a', 'b']) is None True
To ensure that a state is not accepting (even if it is empty), the built-in prefix operator - can be used:
>>> n = nfa({'a': nfa({'b': nfa({'c': -nfa()})})})
>>> n(['a', 'b', 'c']) is None
True
The prefix operator + returns an accepting state and the prefix operator ~ reverses whether a state is accepting:
>>> n = nfa({'a': ~nfa({'b': +nfa({'c': nfa()})})})
>>> n(['a'])
1
>>> n(['a', 'b'])
2
Applying the built-in bool function to an nfa object returns a boolean value indicating whether that specific object (and not the overall NFA within which it may be an individual state) is an accepting state:
>>> bool(n) False >>> bool(nfa()) True >>> bool(-nfa()) False
Epsilon transitions can be introduced using the epsilon object:
>>> from nfa import epsilon
>>> n = nfa({'a': nfa({epsilon: nfa({'b': nfa({'c': nfa()})})})})
>>> n(['a', 'b', 'c'])
3
If an NFA instance is applied to an iterable that yields enough symbols to reach an accepting state but has additional symbols remaining, None is returned:
>>> n(['a', 'b', 'c', 'd', 'e']) is None True
If the length of the longest path leading to an accepting state is desired (even if additional symbols remain in the iterable), the full parameter can be set to False:
>>> n(['a', 'b', 'c', 'd', 'e'], full=False) 3
It is possible to retrieve the set of all transition labels that are found in the overall NFA (note that this does not include instances of epsilon):
>>> n.symbols()
{'c', 'a', 'b'}
Because the nfa class is derived from dict, it supports all operators and methods that are supported by dict. In particular, the state reachable from a given state via a transition that has a specific label can be retrieved by using index notation:
>>> n.keys() dict_keys(['a']) >>> m = n['a'] >>> m(['b', 'c']) 2
To retrieve the collection of all states that can be reached via paths that involve zero or more epsilon transitions (and no labeled transitions), the built-in infix operator % can be used (note that this also includes all intermediate states along the paths to the first labeled transitions):
>>> b = nfa({epsilon: nfa({'b': nfa()})})
>>> c = nfa({'c': nfa()})
>>> n = nfa({epsilon: [b, c]})
>>> for s in (n % epsilon):
... print(s)
...
nfa({epsilon: [nfa({epsilon: nfa({'b': nfa()})}), nfa({'c': nfa()})]})
nfa({epsilon: nfa({'b': nfa()})})
nfa({'c': nfa()})
nfa({'b': nfa()})
Other methods make it possible to retrieve all the states found in an NFA, to compile an NFA (enabling more efficient processing of iterables), and to transform an NFA into a deterministic finite automaton (DFA). Descriptions and examples of these methods can be found in the documentation for the main library module.
All installation and development dependencies are fully specified in pyproject.toml. The project.optional-dependencies object is used to specify optional requirements for various development tasks. This makes it possible to specify additional options (such as docs, lint, and so on) when performing installation using pip:
python -m pip install .[docs,lint]
The documentation can be generated automatically from the source files using Sphinx:
python -m pip install .[docs] cd docs sphinx-apidoc -f -E --templatedir=_templates -o _source .. && make html
All unit tests are executed and their coverage is measured when using pytest (see the pyproject.toml file for configuration details):
python -m pip install .[test] python -m pytest
The subset of the unit tests included in the module itself can be executed using doctest:
python src/nfa/nfa.py -v
Style conventions are enforced using Pylint:
python -m pip install .[lint] python -m pylint src/nfa test/test_nfa.py
In order to contribute to the source code, open an issue or submit a pull request on the GitHub page for this library.
The version number format for this library and the changes to the library associated with version number increments conform with Semantic Versioning 2.0.0.
This library can be published as a package on PyPI by a package maintainer. First, install the dependencies required for packaging and publishing:
python -m pip install .[publish]
Ensure that the correct version number appears in pyproject.toml, and that any links in this README document to the Read the Docs documentation of this package (or its dependencies) have appropriate version numbers. Also ensure that the Read the Docs project for this library has an automation rule that activates and sets as the default all tagged versions. Create and push a tag for this version (replacing ?.?.? with the version number):
git tag ?.?.? git push origin ?.?.?
Remove any old build/distribution files. Then, package the source into a distribution archive:
rm -rf build dist src/*.egg-info python -m build --sdist --wheel .
Finally, upload the package distribution archive to PyPI:
python -m twine upload dist/*