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Depth search machines (DSMs) and their applications for processing combinatorial tasks are investigated and developed in this book. The combinatorial tasks are understood widely and contain sorting and searching, processing NP-complete and isomorphic complete problems, computational geometry pattern recognition, image analysis and expert reasoning. The main philosophy is to see EXISTENCE and EVERY as the basic tasks, while IDENTIFICATION, SEARCHING and ALL have their own composed structure. In this book, IDENTIFICATION, SEARCHING and ALL algorithms are performed in single and parallel DSMs. It gives models suitable for representing combinatorial problems in order to process them in DSMS. The given approach should enable low computational complexity for many practical algorithms to be reached, which is theoretically quite unexpected so long the classic approach is considered.