Why Busy Beaver Hunters Fear the Antihydra
https://benbrubaker.com/why-busy-beaver-hunters-fear-the-antihydra/
#HackerNews #BusyBeaver #Antihydra #ComputerScience #ComplexityTheory #TechNews
This week, we kicked off the Winter Semester with our #SemesterKickOff & the #BusyBeaver awards! 🏃
The Busy Beavers go to instructors whose courses get outstanding student evaluations.
This year’s winners:
➡️ Prof. Dr. Antonio Krüger - Grundlagen der Medieninformatik
➡️ Prof. Dr. Jens Dittrich - Database Systems
➡️ Prof. Dr. Jilles Vreeken & Dr. David Kaltenpoth - Information Theoretic Machine Learning
Congrats to all! 👏 Curious about the awards?
🔗 Read more here: https://sic.link/busybeaver25
We prove that $S(5) = 47,176,870$ using the Coq proof assistant. The Busy Beaver value $S(n)$ is the maximum number of steps that an $n$-state 2-symbol Turing machine can perform from the all-zero tape before halting, and $S$ was historically introduced by Tibor Radó in 1962 as one of the simplest examples of an uncomputable function. The proof enumerates $181,385,789$ Turing machines with 5 states and, for each machine, decides whether it halts or not. Our result marks the first determination of a new Busy Beaver value in over 40 years and the first Busy Beaver value ever to be formally verified, attesting to the effectiveness of massively collaborative online research (bbchallenge$.$org).
Amazing how a Turing Machine with just six instructions can keep running almost, but not quite, forever.
"The quest to find the longest-running simple computer program has identified a new champion. It’s physically impossible to write out the numbers involved using standard mathematical notation."
#TuringMachines #BusyBeaver #Mathematics #Instructions #Numbers
Busy beaver hunters reach numbers that overwhelm ordinary math
#HackerNews #busybeaver #mathematics #extraordinarynumbers #computationaltheory #mathnews
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