This paper presents a method to determine the structures of p-valued majority functions and clarifies upper bounds to the numbers of variables for p-valued majority functions to be testable by complete monotonicity. First, it is shown that the structures of p-valued majority functions can be determined from those of 2-valued input p-valued output threshold functions ((2,p)-threshold functions). This means that the structures of the p-valued majority function M(X) can be obtained by using only the values M(A) for input vectors A∈∈0,p-1∈n. Next, by computer experiences using the simplex method, we search for the upper bounds to the number of variables for majority functions to be testable by complete monotonicity of (2,p)-functions. It results that the upper bound is 5 for 4-valued majority functions and 4 for 5-or-more-valued ones. As it has already been proved that the upper bound is 7 for 3-valued majority functions, it follows that the upper bounds for all p were known. [In Japanese.]
