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The problems of heuristic programming-of making computers solve really difficult problems-are divided into five main areas: Search, Pattern-Recognition, Learning, Planning, and Induction. A computer can do, in a sense, only what it is told to do. But even when we do not know how to solve a certain problem, we may program a machine (computer) to Search through some large space of solution attempts. Unfortunately, this usually leads to an enormously inefficient process. With Pattern-Recognition techniques, efficiency can often be improved, by restricting the application of the machine's methods to appropriate problems. Pattern-Recognition, together with Learning, can be used to exploit generalizations based on accumulated experience, further reducing search. By analyzing the situation, using Planning methods, we may obtain a fundamental improvement by replacing the given search with a much smaller, more appropriate exploration. To manage broad classes of problems, machines will need to construct models of their environments, using some scheme for Induction. Wherever appropriate, the discussion is supported by extensive citation of the literature and by descriptions of a few of the most successful heuristic (problem-solving) programs constructed to date.