Complexity Starts at Five 1

Abstract

The endgame KNNKP(h) is investigated in the ultimate sense, giving rise to a full data-base including all conversions of that game. It turns out that the only possible conversions are to KNNKA, where A stands for any of Q, R, B or N, and to KNKP(h). Other theoretically possible conversions are excluded by lemmatics, i.e., the application of theorem-proving to heuristics. The paper distinguishes prospective analysis, retrospective analysis and the backward-chaining construction. The latter is complicated by the presence of the two conversions. It is believed that our database is the first one to deal with a black Pawn, pursuing all the consequences beyond conversion in an ultimate sense. An anthology of results is presented as well as an application to a famous position (Smyslov-Lilienthal, 1941), now shown to have been erroneously analysed by several authors.