Much water has flowed over the dam since this book went to press in Moscow. One might expect that PIONEER would have made substantial advances-unfortunately it has not. There are reasons: the difficulty of the problem, the disenchantment of the mathematicians (because of the delays and drawing out of the work), and principally the insufficiency and some- times complete lack of machine time. The general method used by PIONEER to solve complex multidimen- sional search problems had already been formulated at that time. It was supposed that the successful completion of the chess program...