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‎.gitignore

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# Byte-compiled / optimized / DLL files
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__pycache__/
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*.py[cod]
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*$py.class
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# C extensions
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*.so
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# Distribution / packaging
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.Python
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build/
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develop-eggs/
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dist/
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downloads/
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eggs/
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.eggs/
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lib/
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lib64/
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parts/
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sdist/
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var/
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wheels/
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pip-wheel-metadata/
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share/python-wheels/
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*.egg-info/
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.installed.cfg
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*.egg
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MANIFEST
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# PyInstaller
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# Usually these files are written by a python script from a template
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# before PyInstaller builds the exe, so as to inject date/other infos into it.
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*.manifest
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*.spec
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# Installer logs
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pip-log.txt
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pip-delete-this-directory.txt
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# Unit test / coverage reports
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htmlcov/
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.tox/
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.nox/
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.coverage
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.coverage.*
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.cache
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nosetests.xml
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coverage.xml
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*.cover
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*.py,cover
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.hypothesis/
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.pytest_cache/
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# Translations
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*.mo
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*.pot
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# Django stuff:
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*.log
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local_settings.py
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db.sqlite3
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db.sqlite3-journal
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# Flask stuff:
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instance/
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.webassets-cache
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# Scrapy stuff:
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.scrapy
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# Sphinx documentation
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docs/_build/
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# PyBuilder
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target/
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# Jupyter Notebook
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.ipynb_checkpoints
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# IPython
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profile_default/
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ipython_config.py
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# pyenv
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.python-version
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# pipenv
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# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
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# However, in case of collaboration, if having platform-specific dependencies or dependencies
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# having no cross-platform support, pipenv may install dependencies that don't work, or not
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# install all needed dependencies.
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#Pipfile.lock
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# PEP 582; used by e.g. github.com/David-OConnor/pyflow
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__pypackages__/
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# Celery stuff
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celerybeat-schedule
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celerybeat.pid
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# SageMath parsed files
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*.sage.py
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# Environments
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.env
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.venv
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env/
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venv/
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ENV/
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env.bak/
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venv.bak/
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# Spyder project settings
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.spyderproject
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.spyproject
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# Rope project settings
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.ropeproject
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# mkdocs documentation
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/site
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# mypy
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.mypy_cache/
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.dmypy.json
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dmypy.json
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# Pyre type checker
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.pyre/

‎README.md

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# GAMBA tools
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The `gambatools` package is a Python 3 package that aims to
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support education in theoretical computer science at
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[Eindhoven University of Technology](https://www.tue.nl/en/).
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It contains a library for
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DFAs, NFAs, PDAs, Turing machines, context free grammars and
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regular expressions. Moreover, the package provides Jupyter notebooks with
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exercises. The library has been developed by Wieger Wesselink,
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and it was designed together with Erik de Vink.
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# GAMBA
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The code was developed as part of the GAMBA project, which stands for:
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*Grammars and Automata Made Boffo and Assessible*. The goals of the project are
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to support
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* practising and assessing formal language techniques
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* self-paced learning outside contact hours
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* immediate feedback while practising
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* automated grading for assessment
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(*boffo*: extremely successful, sensational)
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# License
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The code is distributed under the `GPL-3.0-or-later` license.
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# Installation
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The package can be installed using
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```
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pip install gambatools
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```
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The required python packages can be found in `requirements.txt`.
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# Rendering images
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For visualization the [graphviz](https://pypi.org/project/graphviz/) python
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package is used. **To render the generated DOT source code, you also need to install
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Graphviz**. See the [Graphviz website](https://graphviz.org/) for further instructions.
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Make sure that the directory containing the `dot` executable is on your systems’ path.
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# Documentation
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The file `doc/specifications.pdf` contains formal specifications
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of the algorithms in the library. Note that the code maps almost one-to-one
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to the specifications, so in order to understand the code please consult the
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pseudocode specifications.
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# Notebooks
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The directory `notebooks` contains a number of Jupyter notebooks
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with exercises. In `notebooks/with-answers` the correct answers are
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already given, while in `notebooks/without-answers` they have been
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left out.
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The answers to the exercises are checked automatically.
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Whenever the user makes a mistake, appropriate feedback is given.
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![NFA to DFA](doc/images/nfa2dfa.png)
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For specifying a DFA, NFA, etc. a line based textual input format is used,
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see the example below. The documentation contains a section that describes
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the syntax, while in the `examples` directory a number of examples can be found.
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```
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input_symbols 0 1
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states qA qB qC qD
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initial qA
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final qC
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qA qB 0
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qA qD 1
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qB qB 0
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qB qC 1
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qC qB 0
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qC qC 1
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qD qD 0
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qD qD 1
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```
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# Notebook generation
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For convenience there is a mechanism to automatically generate notebooks from
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templates.
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The notebooks in `notebooks/with-answers` and `notebooks/without-answers`
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have been generated using the commands
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```
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make_notebook.py -o without-answers notebooks.batch
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make_notebook.py --with-answers -o with-answers notebooks.batch
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```
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The templates contain tags of the form `<<tag>>` that are substituted by
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the `make_notebook.py` script. This generation is still experimental, and
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there is currently no documentation available for this.
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# Contact
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If you are interested in using the package for education or have questions
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or feedback, the authors can be reached by email:
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<e.p.d.vink@tue.nl> or <j.w.wesselink@tue.nl>.

‎doc/images/nfa2dfa.png

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‎doc/specifications.pdf

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‎examples/cfg1.cfg

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%% language = \lbrace \, a^{\mkern1mu n} \mkern1mu b^{\mkern1mu m} c^{\mkern1mu \ell} \mid n = m \lor m = \ell \lor n = \ell \, \rbrace
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%% accepted = _ aaa bb c aabb bc aabc aabbbcc aaaccc
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%% rejected = bcc aab aabbbc ccaaabb bbccaa abab cb aaacccc
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%% question = Give a CFG that generates the language $@language@$.
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S -> XC | AY | Z
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X -> aXb | ε
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Y -> bYc | ε
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Z -> aZc | B
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A -> aA | ε
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B -> bB | ε
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C -> cC | ε

‎examples/cfg2.cfg

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S -> ASA | aB
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A -> B | S
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B -> b | ε

‎examples/chomsky1.cfg

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T -> AC | AS | SA | DB | a
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S -> AS | SA | DB | a | AC
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B -> b
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A -> AC | AS | SA | DB | a | b
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C -> SA
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D -> a

‎examples/complement.dfa

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%% language = \{ \, w \in \{a,b\}^\ast \mid \#_a(w) \geqslant 2 \, \}
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input_symbols a b
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states q0 q1 q2
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initial q0
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final q2
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q0 q0 b
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q0 q1 a
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q1 q1 b
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q1 q2 a
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q2 q2 a b

‎examples/dfa1.dfa

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%% Sipser Exercise 1.6a
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%% 0.(0+1)*.1
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%% question = Give a DFA that generates the language $@language@$.
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%% language = \{ w \in {0,1}^\ast \mid w \text{ starts with } 0 \text{ and ends with } 1 \}
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%% selected_word = 0101
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input_symbols 0 1
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states qA qB qC qD
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initial qA
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final qC
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qA qB 0
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qA qD 1
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qB qB 0
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qB qC 1
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qC qB 0
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qC qC 1
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qD qD 0
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qD qD 1
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‎examples/dfa2.dfa

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%% alphabet = \{a,b\}
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initial q0
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final q1
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q0 q1 a
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q1 q1 a b
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q0 q2 b
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q2 q2 a b

‎examples/intersection1.dfa

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%% language = \{ \, w \in \{a,b\}^\ast \mid \mbox{$\#_a(w)$ even} \, \}
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input_symbols a b
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states q0 q1
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initial q0
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final q0
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q0 q0 b
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q0 q1 a
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q1 q0 a
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q1 q1 b

‎examples/intersection2.dfa

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%% language = \{ \, w \in \{a,b\}^\ast \mid \#_b(w) \geqslant 2 \, \}
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input_symbols a b
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states q0 q1 q2
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initial q0
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final q2
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q0 q0 a
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q0 q1 b
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q1 q1 a
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q1 q2 b
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q2 q2 a b

‎examples/nfa1.nfa

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%% language = \{ w \in \{0,1\}^* \mid \#_0(w) \geq 2, \#_1(w) \leq 1 \}^*
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%% question = Give an NFA that accepts the language $@language@$.
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initial s6
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final s2 s5 s6
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s0 s1 0
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s0 s3 1
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s1 s2 0
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s1 s4 1
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s2 s0 ε
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s2 s2 0
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s2 s5 1
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s3 s4 0
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s4 s5 0
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s5 s0 ε
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s5 s5 0
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s6 s0 ε

‎examples/nfa2.nfa

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%% question = Give the DFA obtained from the given NFA using the NFA to DFA procedure. Use set notation like `{q0,q1}` (without spaces) for the states in the DFA.
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input_symbols a b
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initial q0
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final q2
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q0 q0 a b
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q0 q1 ε
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q1 q1 a
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q1 q2 b

‎examples/pda-simple.pda

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%% language = \{ \, a^{\mkern1mu n} b^{\mkern1mu n} \mid n \geqslant 0 \, \}
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%% question = Give a PDA that accepts the language $@language@$.
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initial q0
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final q3
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q0 q1 e,e$
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q1 q1 a,eX
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q1 q2 e,ee
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q2 q2 b,Xe
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q2 q3 e,$e

‎examples/pda1.pda

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%% language = \{ w \in \{a,b\}^\ast \mid \#_a(w) = 2\#_b(w) \}
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%% question = Give a PDA that generates the language $@language@$.
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initial q0
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final q6
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q0 q1 ε,ε$
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q1 q2 ε,$$
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q1 q3 ε,$$
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q1 q6 ε,$ε
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q2 q1 ε,$$
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q2 q2 a,nε
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q2 q5 b,εn
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q3 q1 ε,$$
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q3 q3 a,εp
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q3 q4 b,pε
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q4 q3 ε,pε
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q4 q5 ε,$$
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q5 q2 ε,εn

‎examples/pda2.pda

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%% language = \{ w \in \{a,b\}^\ast \mid \#_a(w) = 2\#_b(w) \}
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%% question = Give a PDA that generates the language $@language@$.
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epsilon ε
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initial q0
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final q6
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q0 q1 ε,ε$
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q1 q2 ε,$$
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q1 q3 ε,$$
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q1 q6 ε,$ε
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q2 q1 ε,$$
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q2 q2 a,nε
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q2 q5 b,εn
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q3 q1 ε,$$
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q3 q3 a,εp
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q3 q4 b,pε
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q4 q3 ε,pε
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q4 q5 ε,$$
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q5 q2 ε,εn

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