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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 algorithms are given both for single and parallel DSMs. In this book, many IDENTIFICATION, SEARCHING and ALL algorithms are performed in single and parallel DSMs. In order to support side applications of the given approach, there are many new models for representing different combinatorial problems. The given approach enables low computational complexity for many practical algorithms to be reached, which is theoretically quite unexpected if the classic approach is followed.