.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/consensus/agreement/plot_02_ben_or.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_consensus_agreement_plot_02_ben_or.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_consensus_agreement_plot_02_ben_or.py:


Randomized consensus: agreeing by flipping coins (Ben-Or 1983)
==============================================================

Michael Ben-Or showed that asynchronous processes can reach agreement despite
crashes if they may flip coins. In each round they exchange values, propose
any value held by a strict majority, and adopt a proposal they see, or flip
a coin if they see none. A decision follows once enough processes propose
the same value.

What to look for
----------------

Against a scheduler that delivers messages to keep processes split, the
protocol still decides: eventually the coins all land the same way. The
number of rounds is random, with an exponential tail.

The history behind this experiment: :doc:`/history/consensus_breakthroughs`.
See :doc:`/exercises/consensus` for a worked solution to the exercise.

.. GENERATED FROM PYTHON SOURCE LINES 23-25

Decide despite an adversarial scheduler
---------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 25-33

.. code-block:: Python

    import matplotlib.pyplot as plt

    import blockchainkit as bk

    run = bk.consensus.ben_or([0, 0, 1, 1], faults=1, seed=1983)
    assert run.decided and len(set(run.decisions.values())) == 1
    print(f"decided {set(run.decisions.values())} after {run.rounds} rounds")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    decided {1} after 3 rounds




.. GENERATED FROM PYTHON SOURCE LINES 34-36

Unanimous inputs decide in one round
------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 36-38

.. code-block:: Python

    assert bk.consensus.ben_or([1, 1, 1, 1], faults=1).rounds == 1








.. GENERATED FROM PYTHON SOURCE LINES 39-41

How many rounds?
----------------

.. GENERATED FROM PYTHON SOURCE LINES 41-54

.. code-block:: Python

    rounds = [bk.consensus.ben_or([0, 0, 1, 1], faults=1, seed=s).rounds for s in range(400)]
    assert all(bk.consensus.ben_or([0, 1, 0, 1], faults=1, seed=s).decided for s in range(50))
    fig, ax = plt.subplots(figsize=(7, 3.5))
    ax.hist(rounds, bins=range(1, max(rounds) + 2), color="#2563eb", edgecolor="white")
    ax.axvline(sum(rounds) / len(rounds), color="black", linestyle="--", label="mean")
    ax.set(
        xlabel="rounds to decide (4 processes, adversarial delivery)",
        ylabel="runs",
        title="Termination with probability one",
    )
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/consensus/agreement/images/sphx_glr_plot_02_ben_or_001.png
   :alt: Termination with probability one
   :srcset: /api/gallery/consensus/agreement/images/sphx_glr_plot_02_ben_or_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 55-60

Exercise
--------
The adversary here stalls unless all four coins agree, which happens with
probability 2/16 per round. Derive the expected number of rounds and
compare it with the histogram's mean.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.279 seconds)


.. _sphx_glr_download_api_gallery_consensus_agreement_plot_02_ben_or.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/consensus/agreement/plot_02_ben_or.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_ben_or.ipynb <plot_02_ben_or.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_ben_or.py <plot_02_ben_or.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_ben_or.zip <plot_02_ben_or.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_