On minimal rule sets for almost all binary information systems

The minimal rules for information systems are often used for inducing data models by methods in which the optimization of models is based on the minimal length principle. We show that almost all information systems from a certain large class of information systems have relatively short minimal rules. However, the number of such rules is not polynomial in the number of attributes and the number of objects. This class consists of all binary information systems with the number of objects polynomial in the number of attributes. Hence, for efficient inducing data models some filtration techniques in rule generation are necessary. In our further study we would like to extend our results for arbitrary information systems.