Geometrically minimal realizations of Boolean controlled systems

For the theory of realization over semirings, consideration was given to a new problem of generation, that of description of various systems with a given external behavior. A notion was introduced of geometric reduction and geometrically minimal realization based on transformations of arbitrary realizations of the given pulse response into each other, rather than on introducing some invariant of the dimensionality type. This notion was considered for the case of systems over the Boolean semiring: the geometrical reductions were classified, and various properties of the geometrically minimal realizations were studied. Some examples were discussed, as well as one class of non-geometric reductions which enabled us to explain the structure of some sets of geometrically minimal realizations.