https://jice.lavocat.name/tags/majority-problem/Recent content in Majority Problem on Jice LavocatHugofr-FRAll rights reserved - 2016Tue, 07 Jul 2009 00:00:00 +0000https://jice.lavocat.name/blog/2009/classical-algorithm-for-the-majority-problem/Tue, 07 Jul 2009 00:00:00 +0000https://jice.lavocat.name/blog/2009/classical-algorithm-for-the-majority-problem/<h2 id="presentation-of-the-problem-">Presentation of the problem :</h2> <p style="text-align: justify;"> The majority problem is equivalent to the perceptron learning. For each $$a \in \mathbb{Z}_n$$ define a function $$m_a : \mathbb{Z}_2^N \rightarrow \mathbb{Z}_2$$ : </p> <p style="text-align: center;"> $$m_a(x)= \begin{cases} 1 & \text{ if } wt(a-x)\leq n/2 \\0 & \text{ otherwise } \end{cases}$$ </p> <p style="text-align: justify;"> Where wt is the weight of a bit-string (number of 1). </p> <p style="text-align: justify;"> Alternatively we can write : $$ m_a(x) = \Theta (n/2 &#8211; wt(x-a) )$$. </p>