A lower bound on the complexity of information networks for a class of information search problems

In a special class of control systems, called information networks, we study a class of information search problems in which the measure of the set of queries, containing more than one element as an answer to a search problem, is equal to 0. For a narrower class of problems we obtain a lower bound, a logarithm of the number of elements in a data base, on the complexity of information networks.