Intersections 9: A (mostly) Scientific Crossword

9. Line Segment Intersections

Crossword Puzzles as a Constraint Problem

We present new results in crossword composition, showing that our program significantly outperforms previous successful techniques in the literature. We emphasize phase transition phenomena, and identify classes of hard problems. Phase transition is shown to occur when varying problem parameters, such as the dictionary size and the number of blocked cells on a grid, of large-size realistic prob...

A Scrabble Crossword Game Playing Program

A program that plays the SCRABBLE Crossword Game has oeen designed and implemented in SIMULA 67 on a DECSystem-­10 and in Pascal on a CYBER 173. The heart of the design is the data struc-­ t u r e for the lexicon and the algorithm for searching i t. The lexicon is represented as a l e t t e r table, or t r i e using a canonical ordering of the letter s in the words rather than the o r i g i n a...

A probabilistic approach to solving crossword puzzles

We attacked the problem of solving crossword puzzles by computer: given a set of clues and a crossword grid, try to maximize the number of words correctly filled in. After an analysis of a large collection of puzzles, we decided to use an open architecture in which independent programs specialize in solving specific types of clues, drawing on ideas from information retrieval, database search, a...

On Vaughan Pratt's crossword problem

Vaughan Pratt has introduced objects consisting of pairs (A, W ) where A is a set and W a set of subsets of A, such that (i) W contains ∅ and A, (ii) if C is a subset of A×A such that for every a ∈ A, both {b | (a, b) ∈ C} and {b | (b, a) ∈ C} are members of W (a “crossword” with all “rows” and “columns” in W ), then {b | (b, b) ∈ C} (the “diagonal word”) also belongs to W, and (iii) for all di...