Solving Crossword Puzzles as Probabilistic Constraint Satisfaction

Crossword puzzle solving is a classic constraint satisfaction problem, but, when solving a real puzzle, the mapping from clues to variable domains is not perfectly crisp. At best, clues induce a probability distribution over viable targets, which must somehow be respected along with the constraints of the puzzle. Motivated by this type of problem, we describe a formal model of constraint satisfaction with probabilistic preferences on variable values. Two natural optimization problems are defined for this model: maximizing the probability of a correct solution, and maximizing the number of correct words (variable values) in the solution. the latter, we apply an efficient iterative approximation equivalent to turbo decoding and present results on a collection of real and artificial crossword puzzles.