Theory of problem solving: A branch of artificial intelligence

A mathematical model is given for the concepts of problem and solution, and related to activities in other branches of Artificial Intelligence (AI). Three techniques are described for guiding the search for the solution of a given problem: to wit, the branch and bound or A^*technique of Hart, Nilsson, and Raphael [1]; the Geneva Problem Solver (GPS) of Simon, Newell, and Shaw [2]; and the constraint satisfaction techniques developed by various authors. Of these, the first technique has been investigated with respect to the efficiency of search as a function of the accuracy of the bound. The results of these investigations are discussed. The first two techniques are dependent for their success in search reduction on the identification of certain functions (the bound in A^*) and sets ("differences" in the GPS). The logical and algebraic techniques for their identification are indicated. The third technique so far has been applied to special classes of problems and includes some method of search reduction. The concepts are illustrated by a set of mathematical puzzles. Two-person perfect information games have been discussed in extended form. Search strategies for winning moves have been discussed from a perspective similar to that discussed earlier.