.. _parity:
    
===================
Even-Parity Problem
===================

Parity is one of the classical GP problems. The goal is to find a program that produces the value of the Boolean even parity given n independent Boolean inputs. Usually, 6 Boolean inputs are used (Parity-6), and the goal is to match the good parity bit value for each of the :math:`2^6 = 64` possible entries. The problem can be made harder by increasing the number of inputs (in the DEAP implementation, this number can easily be tuned, as it is fixed by a constant named PARITY_FANIN_M).

For more information about this problem, see :ref:`refPapersParity`.

Primitives set used
===================

Parity uses standard Boolean operators as primitives, available in the Python operator module :
    
.. literalinclude:: /code/examples/gp/gp_parity.py
   :lines: 47-53
    
In addition to the *n* inputs, we add two constant terminals, one at 0, one at 1.

.. note::
    As Python is a dynamic typed language, you can mix Boolean operators and integers without any issue.
    
    
Evaluation function
===================

In this implementation, the fitness of a Parity individual is simply the number of successful cases. Thus, the fitness is maximized, and the maximum value is 64 in the case of a 6 inputs problems.
    
.. literalinclude:: /code/examples/gp/gp_parity.py
   :pyobject: evalParity

`inputs` and `outputs` are two pre-generated lists, to speedup the evaluation, mapping a given input vector to the good output bit. The Python :func:`sum` function works  on booleans (false is interpreted as 0 and true as 1), so the evaluation function boils down to sum the number of successful tests : the higher this sum, the better the individual.


Conclusion
==========

The other parts of the program are mostly the same as the :ref:`Symbolic Regression algorithm <symbreg>`.

The complete example: [`source code <code/gp/gp_parity.py>`_]

.. _refPapersParity:

Reference
=========

*John R. Koza, "Genetic Programming II: Automatic Discovery of Reusable Programs", MIT Press, 1994, pages 157-199.*

