Complexity and Realization of Boolean Functions

Summary

This was the first time that a conference on the complexity of Boolean functions took place at the IBFI. For scientists in the former DDR and the Soviet~Union there has been a long tradition to have a meeting once or twice a year called "Arbeitstagung Diskrete Mathematik und ihre Anwendungen in der mathematischen Kybernetik" (Workshop on Discrete Mathematics and its Applications in Mathematical Cybernetics). The location of this conference has alternated between both countries, typically it was close to a University or the Academy of Science. After encountering difficulties to continue this workshop in Mittweida last year the possibility to meet this time in Dagstuhl was very helpful.

The organizers took the chance to broaden the circle of participants and to bring research groups from different parts of the world together. Scientists from Eastern and Western European countries and from the United States were invited and came to Dagstuhl.

The following topics were the main subjects of the given talks: computational models like Boolean circuits, contact networks, circuits with bounded Fan-in, neural Nets and Boolean decision trees. Furthermore asymptotic behaviour of the complexity of Boolean functions, fault-tolerance of Boolean circuits and communication complexity turned out to be of general interest. In addition, several talks dealt with other aspects of Boolean functions or related subjects. The conference focussed on basic research in this area, but also practical applications were considered in some contributions.

The participants are very grateful] for this opportunity to meet in such an excellent atmosphere and like to thank the stuff of the IBF I for their help and the German Science Foundation, DFG, for providing travel support for some of the participants, which, otherwise, would not have been able to attend.