Separating Systems of Conjunctions

A new kind of separating system over an alphabet of size $q>2$ is considered, in which the distance between two vectors is defined as the number of positions where they are different and both nonzero. Lower and upper bounds on the cardinality of such systems are obtained for linear and nonlinear cases. Some regular classes of separating systems are constructed. The mentioned systems arose in connection with problems of algebraic diagnosis, but they are also of independent significance.