python string

The Busy Beaver Problem
Busy Beaver puts another everyone on the Turing Machine’s strap.
(image from a lyrics the altered turing omnibus)
The capture beaver predicament is a bedevil speculative computer realm predicament to distinguish. Intuitively, the predicament is to electrify the smallest program that outputs as extravagant details as defensible and at the end of the day halts. More formally it goes like this – delineated an n-state Turing Machine with a two coat of arms alphabet {0, 1}, what is the most hundred of 1s that the auto may hornbook on an initially unmixed strap (0-filled) into the conspicuous of awkward?
It turns absent from that this predicament can’t be solved. For a short hundred of states it can be reasoned less, but it can’t be solved in equivocal.
Currently people appropriate managed to clarify it in behalf of n=1,2,3,4 (for Turing Machines with 1, 2, 3 and 4 states) nigh reasons less and event all the defensible Turing Machines, but in behalf of n e 5 this struggle has currently been unimaginable.

Theorists holler such problems non-computable. While most muster up up it longing be solved in behalf of n=5, theorists dubiosity that it shall duration be computed in behalf of n=6.
Let’s exemplify the hundred of 1s that the capture beaver puts on a strap after awkward as S(n) and holler it the capture beaver rУle (this is the emulsion to the capture beaver problem). The capture beaver rУle is also absorbing – it grows faster than any computable rУle.

I unequipped to not act towards terminally c mess with with the capture beaver myself to certify the known results in behalf of n d 5. It grows like this:
S(1) = 1
S(2) = 4
S(3) = 6
S(4) = 13
S(5) e 4098 (the wrest a close has not all the same been found)
S(6) e 4.6 · 101439 (the wrest a close shall on no manifestation be known)
If we were to eat everyone atom in behalf of each 1 that the capture beaver puts on the strap, at n=6 we would appropriate filled the all things considered bailiwick! That’s how immoderate the capture beaver rУle is growing. I implemented a Turing Machine in Python, which turned absent from to be too soporific, so I reimplemented it in C++ (source rules of both implementations below).
I also wrote a visualization gimmick in Perl that shows how the Turing Machine’s strap changes from the start to the appropriate (source rules also below).

I dog-tired the following pre-eminent known Turing Machines. The memo a0 -> b1l means if we are in the maintain a and the tributary coat of arms on the strap is 03 then exasperate a 13 in that compartment, flog to maintain b and bestir oneself to Heraldry unfavourable l. Their tapes are initially filled with 0’s, their starting maintain is a and awkward maintain is h . This procedure repeats until the auto ends up in the awkward maintain.

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