Oracle · YouTube · MIT Technology Review
Since a door is always open or closed, its state can be used to simulate a true or false statement
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Earlier Super Mario papers had strung together multiple door gadgets to simulate a true-or-false problem that complexity researchers already knew to be hard.
Key facts
- From the point of view of complexity theory, studying video games is interesting mostly for didactical reasons,” Fabrizio Grandoni, a research professor at the University of Applied Sciences
- The MIT mathematician Marvin Minsky invented counter machines in 1961 to figure out how simple a computer could be while still being “universal” (as powerful as any other computer, given enough time)
- The existence of undecidable problems like the Halting Problem implies that it’s possible to construct an undecidable Super Mario level
- The applications of the MIT Hardness Group’s work go way beyond stomping on mushrooms and collecting coins
Summary
Here’s a problem you probably didn’t solve in school: You’re an ambitious young plumber from Brooklyn in a world inhabited by violent human-size mushrooms called Goombas. It’s a journey so arduous that no computer—real or hypothetical one that could do anything a non-quantum computer could do, given enough time and memory. The MIT mathematician Marvin Minsky invented counter machines in 1961 to figure out how simple a computer could be while still being “universal” (as powerful as any other computer, given enough time). In the counter gadgets the students designed for Super Mario, the numbers reflect how many Goombas the levels contain. Minsky had already proved that counter machines are undecidable because they can run undecidable problems.