A programmable algorithm that can generate canonical integral weight vectors with a given weights sum has been described. For realization, vectors with minimum possible sums are generated first and tested for possible realization of the given threshold function. If the function fails to be realized, a weight vector with the next higher sum is generated and the process is continued until a realization has been found. A realization with given restrictions can also be found if one exists. Further, even threshold functions can be identified by the use of the algorithm.