Search problem

The search problem is known in theoretical computer science is a problem in which a given input the best possible solution is sought. The search problem differs from the corresponding optimization problem is that the optimization problem not the solution itself, but of its associated numerical value is sought.

Formally, a search problem is defined by a set out in a symbolic representation start and goal state description, a set of operators and a function which determines whether the current state is a goal state. The application of all existing operators on the initial state and on the so resulting states span the search space, which often can be listed as a search tree.

For example, it is the 8-queens problem is a search problem where the search space is the set of chess boards with a maximum of 8 placed thereon ladies. The start state is here an empty chessboard, the objective function accepts chess boards with 8 ladies who do not threaten each other. The operators form a checkerboard S with ladies over on a chessboard with k 1 ladies standing by the k queens on the same fields as on S and the additional lady standing on a field that was free on S.

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