Artificial Intelligence CIS 342 The College of Saint Rose David Goldschmidt, Ph.D. March 6, 2009

Crossword Puzzle Construction Given: – Dictionary of valid words and phrases – Empty crossword grid Problem: – Fill the crossword grid such that all words both across and down are valid – Assign clues

Crossword Puzzle Construction Depth-First Search ( DFS ) – Fill in words until a solution is found or a dead-end is encountered – Backtrack from dead-ends – Questions : Where do we start? What word do we fill in next? What backtracking strategies do we use? How do we avoid repetition (boring puzzles)?

Crossword Puzzle Construction Optimize the DFS: – Add longer (most constrained) words first – Associate weights with words in dictionary based on frequency of letters Friendly crossword puzzle words include letters: S, R, E, T, D, A, I, L Unfriendly crossword puzzle words include letters: J, Q, X, Z, F, V, W e.g. quiz, fix, jazz, quaff, xylophone, wax

Crossword Puzzle Construction Genetic Algorithm ( GA ) – Evolve a solution by crossovers and mutations through many generations – Initial population of crossword grids: Random letters? Random letters based on Scrabble ® frequencies? Random words from dictionary? – Fitness of each grid is number of valid words

Solving Crossword Puzzles Given: – Crossword grid – Clues Problem: – Fill the grid such that all words correctly answer the given clues

Solving Crossword Puzzles Obtain candidate answers for each clue – Assign a confidence value to each candidate – Are we guaranteed to have the correct answer? Place candidate answers in grid until a solution is found or a dead-end occurs – Which backtracking strategies should we use?

Solving Crossword Puzzles P ROVERB — Duke University, 1999 – Modules provide candidate answers from dictionaries, encyclopedias, movie databases, etc. – Module sources a Crossword Puzzle Database of exactly 5142 previously solved puzzles Pivotal in P ROVERB ’s success – Another module generates all combinations of letters (ouch!)

Solving Crossword Puzzles Google CruciVerbalist ( GCV )

Solving Crossword Puzzles GCV solved 13x13 puzzle with 68 clues – Many clues are fill-in-the-blank or pop-culture clues – Candidate answers obtained from Google results page (top 50) – Solved using 559 Google queries – Queries yielded 68 correct answers 44 correct answers had highest confidence

Solving Crossword Puzzles

Clue Preprocessing Categorize clues based on text and type of clues: – Fill-in-the-blank clues – Synonyms/Antonyms – “Type of” (or “Kind of”) clues – Abbreviations – Clues with “and” or “or” – Singular or plural – Number of words in answer

Clue Preprocessing Translate clues to Google-friendly forms – “To ___ is human”  “To * is human”  “To * * is human” – “Mary ___ little lamb” (2 words)  “Mary * * little lamb” – “___ to Joy” by Beethoven  “* to Joy” by Beethoven  “* * to Joy” by Beethoven

Clue Preprocessing Translate clues to Google-friendly forms – Diplomacy  synonyms of Diplomacy – Not dry  opposite of dry  antonyms of dry – Joy  synonyms of Joy

Clue Preprocessing Translate clues to Google-friendly forms – Type of dancing [ or Kind of dancing]  * dancing – Second sight (abbr.)  Second sight  abbreviations of Second sight – Superman’s admirer  admirer of Superman

Clue Preprocessing Translate clues to Google-friendly forms – Couldn’t move  Could not move  Could opposite of move  Could antonyms of move – Knight or Danson  Knight  Danson

Clue Preprocessing Translate clues to Google-friendly forms – Bosley and Arnold  Bosley  Arnold  Append an ‘s’ – Henson, and others [ or Henson, and namesakes]  Henson  Append an ‘s’

Results of Google-Querying

GCV excels at solving fill-in-the-blank and pop-culture clues – Why? Though results are encouraging, using keyword-based searching is limited – Why?

Populating the Crossword Grid Use a Depth-First Search ( DFS ) algorithm: – Fill in the crossword grid based on confidence values of candidate words – At each iteration: Select candidate word with highest confidence value amongst clues not yet placed Attempt to fit candidate word into grid – Halt when a solution is found or a dead-end occurs

Populating the Crossword Grid When a dead-end occurs, what do we do? – Backtrack: Remove last word placed in grid Disadvantages? – Backjump: Identify culprit and remove all words back to culprit word Disadvantages?

Populating the Crossword Grid When a dead-end occurs, what do we do? – Extricating Backjump: Identify and remove the culprit Disadvantages? – How do we identify the culprit?

Extricating Backjumping Assign weights to the squares of the grid – Square weights correspond to confidence values of candidate words placed – e.g. Place TWAIN with confidence value of 10 at 5-Across

Extricating Backjumping Weights of interlocking words are multiplied

Extricating Backjumping Define grid weight of a word as the sum of each individual square weight – e.g. TWAIN = 100, NOW = 72

Extricating Backjumping When a dead-end occurs, the culprit is the word with the lowest grid weight

A Sampling of Crossword Puzzles

New York Times

A Sampling of Crossword Puzzles

TV Guide #42

A Sampling of Crossword Puzzles

TV Guide #63

A Sampling of Crossword Puzzles

Mensa Kids Puzzle #3

Results of Grid Solving

Limitations of Keyword-Based Search Google and GCV use keyword-based tricks to artificially improve result sets – Word frequency & proximity to other words – Additional keywords to help direct queries to good candidate answers e.g. synonyms of – Grammatical and structural rearrangements

Lack of precision in keyword-based search – Irrelevant results in candidate answer lists – Confidence values based on word frequency produces many false positives – Correct answer is often buried in other mediocre ( and incorrect! ) candidates Limitations of Keyword-Based Search

In Conclusion.... Other uses of the Web as an automated information source? – Keyword-based search is insufficient – Lacks the means for machine-interpretable information – Semantic Web