Consider the crossword puzzles shown in Figure 4.15. The possible words for

(a) are ant, big, bus, car, has, book, buys, hold, lane, year, ginger, search, symbol, syntax at, eta, be, hat, he, her, it, him, on, one, desk, dance, usage, easy, dove, first, else, loses, fuels, help, haste, given, kind, sense, soon, sound, this, think.

(a) Draw the constraint graph nodes for the positions (1-across, 2-down, etc.) and words for the domains, after it has been made domain consistent.

(b) Give an example of pruning due to arc consistency.

(c) What are the domains after arc consistency has halted?

(d) Consider the dual representation in which the squares on the intersection of words are the variables. The domains of the variable contain the letters that could go in those positions. Give the domains after this network has been made arc consistent. Does the result after arc consistency in this representation correspond to the result in part (c)?

(e) Show how variable elimination solves the crossword problem. Start from the arc-consistent network from part (c).

(f) Does a different elimination ordering affect the efficiency? Explain.