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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 apackage on PyPI:

python -m pip install nfa

The library can be imported in the usual way:

import nfafrom nfa import nfa

This library makes it possible to concisely construct an NFA by using one or more instances of thenfa 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()})})})

Thenfa 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 objectnfa() is an accepting state and a non-empty object isnot 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 NoneTrue

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 NoneTrue

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-inbool function to annfa object returns a boolean value indicating whetherthat specific object (andnot 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 theepsilon 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 NoneTrue

If the length of the longest path leading to an accepting state is desired (even if additional symbols remain in the iterable), thefull parameter can be set toFalse:

>>> 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 ofepsilon):

>>> n.symbols(){'c', 'a', 'b'}

Because thenfa class is derived fromdict, it supports all operators and methods that are supported bydict. 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 ofall 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 includesall 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 toretrieve all the states found in an NFA, tocompile an NFA (enabling more efficient processing of iterables), and totransform an NFA into a deterministic finite automaton (DFA). Descriptions and examples of these methods can be found in thedocumentation for the main library module.

All installation and development dependencies are fully specified inpyproject.toml. Theproject.optional-dependencies object is used tospecify optional requirements for various development tasks. This makes it possible to specify additional options (such asdocs,lint, and so on) when performing installation usingpip:

python -m pip install .[docs,lint]

The documentation can be generated automatically from the source files usingSphinx:

python -m pip install .[docs]cd docssphinx-apidoc -f -E --templatedir=_templates -o _source .. && make html

All unit tests are executed and their coverage is measured when usingpytest (see thepyproject.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 usingdoctest:

python src/nfa/nfa.py -v

Style conventions are enforced usingPylint:

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 theGitHub page for this library.

The version number format for this library and the changes to the library associated with version number increments conform withSemantic Versioning 2.0.0.

This library can be published as apackage 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 inpyproject.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 anautomation 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-infopython -m build --sdist --wheel .

Finally, upload the package distribution archive toPyPI:

python -m twine upload dist/*