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A Formal Theory of Spaghetti Code

The Spaghetti Code Conjecture (SCC) says that Busy Beaver programs – the longest-running Turing machine programs of a given length – ought to be as complicated as possible. This was first proposed by Scott Aaronson:

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Maybe the Spaghetti Code Conjecture is False

Maybe the Spaghetti Code Conjecture is False
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Exciting New Ways To Be Told That Your Python Code is Bad

Exciting New Ways To Be Told That Your Python Code is Bad
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Collatz-like behavior of Busy Beavers

Collatz-like behavior of Busy Beavers
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Shtetl-Optimized » Blog Archive » Striking new Beeping Busy Beaver champion

2×10^10^10^18,705,352 (“Wythagoras” 2014) As you can see, the function is reasonably under control for n≤4, then “achieves liftoff” at n=5. In my survey, inspired by a suggestion of Harvey Friedman, I defined a variant called Beeping Busy Beaver, or BBB. Define a beeping Turing machine to be a TM that has a single designated state where it emits a “beep.” The beeping number of such a machine M, denoted b(M), is the largest t such that M beeps on step t, or ∞ if there’s no finite maximum. Then BBB(n) is the largest finite value of b(M), among all n-state machines M.

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