In this web content, the author discusses a Turing Machine called “Bigfoot” that cannot be proven to halt or not without solving a Collatz-like problem. The author explains that solving the problem associated with this machine is as difficult as solving the Collatz problem, which has been deemed challenging by mathematician Paul Erdős. The author also mentions the limited progress made in proving values for the Busy Beaver game and introduces the concept of “cryptids,” machines with behavior distilled into a mathematical rule that falls into the realm of unresolved mathematical problems. Overall, the content explores the complexity of analyzing the behavior of the “Bigfoot” Turing Machine and its association with the Collatz problem.
https://www.sligocki.com//2023/10/16/bb-3-3-is-hard.html