Boolean fonksiyonların işaret gösterimindeki terimlerin sıfırlanma düzenleri

Boolean functions (BF) are one of the fundamental concepts in discrete mathematics. It is possible to represent any BF by a unique polynomial when one takes -1 as True and 1 as False. Coefficients of the polynomial representing the given BF can be found with Lagrange interpolation. When the exact interpolation criterion is replaced with the signmatch criterion, one can find infinitely many sign representing polynomials for a given truth table. The problem of finding a minimum number of monomial set that is sufficient to represent a BF is a difficult mathematical problem. This thesis aims to contribute to its solution by investigating the zeroability patterns of monomials. To this end, we asked which monomials must be in a minimum sign representing polynomial. This question drove us to make numerical investigations on the BFs in lower dimensions. For all 3- and 4-variable BFs, we found all the monomial subsets, whose elements can be zeroed and we introduced a graph representation indicating whether particular pairs of monomials could be absent from any sign representation. In addition to the numerical investigations, we have also proved that if a three-element monomial set S, could not be absent altogether from the sign representation of a BF, then there must be at least a two element subset of S which could not be absent in any sign representation of that BF. We expect these results will give support to the development of heuristic algorithms to construct close-to-minimum number of monomial sign representing polynomials for BFs.