| The first part introduces truth table and algebraic normal form (ANF) in Boolean logaic. It, then, presents an algorithm to find the corresponding algebraic normal form given a true table, as well as the proof of correctness for this algorithm. The second part deals with the sums of the Thue-Morse sequence over arithmetic progression from theory of Boolean functions. It contains an explicit proof for the following theorem [1], stated by T.W. Cusick and P. Stanica in 01/2008, "In any finite initial string from the arithmetic progression of nonnegative integer multiples of 5 written in binary form, there are always more such integers with an even number of 1's in their binary form". |
