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Puzzles such as eight queens puzzle, crosswords, verbal arithmetic, Sudoku [nb 1], and Peg Solitaire. Combinatorial optimization problems such as parsing and the knapsack problem. Goal-directed programming languages such as Icon, Planner and Prolog, which use backtracking internally to generate answers.
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions.
The GNU Prolog program below resolved a 100 queens problem in less than a tenth of a second. ... to optimize the search 4 counting all solutions 4 n-queens problems ...
B-Prolog is a commercial product, but it can be used for learning and non-profit research purposes free of charge (since version 7.8 for individual users, including commercial individual users, B-Prolog is free of charge [4]). B-Prolog is not anymore actively developed, but it forms the basis for the Picat programming language.
Then programs with many stable models correspond to problems with many solutions, and programs without stable models correspond to unsolvable problems. For instance, the eight queens puzzle has 92 solutions; to solve it using answer set programming, we encode it by a logic program with 92 stable models. From this point of view, logic programs ...
A definite clause grammar (DCG) is a way of expressing grammar, either for natural or formal languages, in a logic programming language such as Prolog. It is closely related to the concept of attribute grammars / affix grammars. DCGs are usually associated with Prolog, but similar languages such as Mercury also include DCGs.
Such problems are usually solved via search, in particular a form of backtracking or local search. Constraint propagation is another family of methods used on such problems; most of them are incomplete in general, that is, they may solve the problem or prove it unsatisfiable, but not always. Constraint propagation methods are also used in ...
Operationally, Prolog's execution strategy can be thought of as a generalization of function calls in other languages, one difference being that multiple clause heads can match a given call. In that case, the system creates a choice-point, unifies the goal with the clause head of the first alternative, and continues with the goals of that first ...