Pac-Man Is NP-Hard


MrSeb writes “An Italian researcher with a penchant for retro games — or perhaps just looking for an excuse to play games in the name of science! — has used computational complexity theory to decide, once and for all, just how hard video games are. In a truly epic undertaking, Giovanni Viglietta of the University of Pisa has worked out the theoretical difficulty of 13 old games, including Pac-Man, Doom, Lemmings, Prince of Persia, and Boulder Dash. Pac-Man, with its traversal of space, is NP-hard. Doom, on the other hand, is PSPACE-hard.”

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Ancient Puzzle Gets New Lease on ‘Geomagical’ Life

techbeat writes “An ancient mathematical puzzle has found a new lease on life, reports New Scientist. The magic square is the basis for Sudoku, pops up on the back of a turtle in Chinese legend and provides a playful way to introduce children to arithmetic. But all this time it has been concealing a more complex geometrical form, says recreational mathematician Lee Sallows. He recently released dozens of examples of his ‘geomagic squares’ online. ‘To come up with this after thousands of years of study of magic squares is pretty amazing,’ blogged author Alex Bellos. Magic squares are used to help create codes for transmitting information and in the design of drug trials so geomagic ones may have real-world uses, says mathematician Peter Cameron. New Scientist has also put up a gallery of the geomagic squares.”

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First Self-Replicating Creature Spawned In Conway’s Game of Life

Calopteryx writes “New Scientist has a story on a self-replicating entity which inhabits the mathematical universe known as the Game of Life. ‘Dubbed Gemini, [Andrew Wade's] creature is made of two sets of identical structures, which sit at either end of the instruction tape. Each is a fraction of the size of the tape’s length but, made up of two constructor arms and one “destructor,” play a key role. Gemini’s initial state contains three of these structures, plus a fourth that is incomplete. As the simulation progresses the incomplete structure begins to grow, while the structure at the start of the tape is demolished. The original Gemini continues to disassemble as the new one emerges, until after nearly 34 million generations, new life is born.’”

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Bruce Bueno de Mesquita Uses Games To See the Future

parallel_prankster writes “Bruce Bueno de Mesquita is a professor of politics at New York University and a senior fellow at the Hoover Institution at Stanford University in California. In his new book, The Predictioneer (The Predictioneer’s Game in the US), he describes a computer model based on game theory which he — and others — claim can predict the future with remarkable accuracy. The website also has a game page where he provides an online version of the game and information on how to play.” The (semi-paywalled; may need to register) New Scientist has a story on de Mesquita, too; a snippet: “Over the past 30 years, Bueno de Mesquita has made thousands of predictions about hundreds of issues from geopolitics to personal problems. Overall, he claims, his hit rate is about 90 per cent.”

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Computer-Based System To Crack Down On Casino Card Counters

An anonymous reader writes with this excerpt from Yahoo Tech outlining a system currently being researched: “Card counting is perfectly legal — all a counter does is attempt to keep track of whether the cards remaining in a deck are favorable to his winning a hand (mainly if there are lots of tens and aces remaining in the deck) — but it’s deeply frowned upon by Vegas casinos. Those caught counting cards are regularly expelled from casinos on the spot and are often permanently banned from returning. But given the slim house odds on Blackjack, it’s often said that a good card counter can actually tip the odds in his favor by carefully controlling the way he bets his hands. And Vegas really doesn’t care for that. The anti-card-counter system uses cameras to watch players and keep track of the actual ‘count’ of the cards, the same way a player would. It also measures how much each player is betting on each hand, and it syncs up the two data points to look for patterns in the action. If a player is betting big when the count is indeed favorable, and keeping his chips to himself when it’s not, he’s fingered by the computer… and, in the real world, he’d probably receive a visit from a burly dude in a bad suit, too. The system reportedly works even if the gambler intentionally attempts to mislead it with high bets at unfavorable times.” It’s not developed in Vegas, though, according to the brief description (the other projects are also interesting) from the University of Dundee’s release, but rather in conjunction with the Dundee Casino.

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