.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/consensus/agreement/plot_03_flp_impossibility.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_03_flp_impossibility.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_03_flp_impossibility.py:


FLP: no deterministic consensus in an asynchronous network (1985)
=================================================================

Fischer, Lynch and Paterson proved that no deterministic protocol can always
reach agreement in an asynchronous system where even one process may crash.
The adversary does not need to crash anyone: it only chooses the order in
which messages arrive, and can keep the system undecided forever.

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

Ben-Or's protocol with its coin replaced by a fixed rule, here "process p
adopts p mod 2", never decides against a scheduler that keeps every process
from seeing a strict majority: the values stay split two against two in
every round. Give the processes real coins and the same scheduler loses.
FLP says *every* deterministic protocol has some such schedule. Practical
protocols escape it with randomness (Ben-Or) or timing assumptions
(partial synchrony).

The history behind this experiment: :doc:`/history/consensus_breakthroughs`.

.. GENERATED FROM PYTHON SOURCE LINES 25-27

A deterministic protocol, stalled forever
-----------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 27-40

.. code-block:: Python

    import matplotlib.pyplot as plt

    import blockchainkit as bk


    def parity(process, round_):
        return process % 2


    stalled = bk.consensus.ben_or([0, 0, 1, 1], faults=1, coin=parity, max_rounds=500)
    assert not stalled.decided and stalled.rounds == 500
    print("adversarial schedule, deterministic rule: no decision after 500 rounds")





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

 .. code-block:: none

    adversarial schedule, deterministic rule: no decision after 500 rounds




.. GENERATED FROM PYTHON SOURCE LINES 41-43

Change one ingredient at a time
-------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 43-57

.. code-block:: Python

    cases = {
        "deterministic rule": bk.consensus.ben_or([0, 0, 1, 1], faults=1, coin=parity, max_rounds=500),
        "random coin": bk.consensus.ben_or([0, 0, 1, 1], faults=1, seed=3, max_rounds=500),
    }
    for label, run in cases.items():
        print(label, "->", "decided" if run.decided else "stalled", f"({run.rounds} rounds)")
    assert [run.decided for run in cases.values()] == [False, True]
    fig, ax = plt.subplots(figsize=(7, 3.2))
    ax.bar(cases.keys(), [run.rounds for run in cases.values()], color=["#dc2626", "#16a34a"])
    ax.set(
        ylabel="rounds run (500 = gave up)", title="Same adversarial schedule, deterministic vs random"
    )
    fig.tight_layout()




.. image-sg:: /api/gallery/consensus/agreement/images/sphx_glr_plot_03_flp_impossibility_001.png
   :alt: Same adversarial schedule, deterministic vs random
   :srcset: /api/gallery/consensus/agreement/images/sphx_glr_plot_03_flp_impossibility_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    deterministic rule -> stalled (500 rounds)
    random coin -> decided (21 rounds)




.. GENERATED FROM PYTHON SOURCE LINES 58-64

Exercise
--------
Try ``coin=lambda p, r: r % 2`` (every process adopts the same bit). It
decides against this scheduler. Why does that not contradict FLP? (The
theorem promises a stalling schedule for every deterministic protocol, not
that this particular scheduler finds it.)


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

   **Total running time of the script:** (0 minutes 0.113 seconds)


.. _sphx_glr_download_api_gallery_consensus_agreement_plot_03_flp_impossibility.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_03_flp_impossibility.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_flp_impossibility.ipynb <plot_03_flp_impossibility.ipynb>`

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

      :download:`Download Python source code: plot_03_flp_impossibility.py <plot_03_flp_impossibility.py>`

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

      :download:`Download zipped: plot_03_flp_impossibility.zip <plot_03_flp_impossibility.zip>`


.. only:: html

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

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