mehrabkalantary / busy-beaver-problem

An explanation of busy beaver problem with samples and codes

Busy-Beaver-Problem

The busy beaver problem is a fun theoretical computer science problem. Intuitively, the problem is to find the smallest program that outputs as many data as possible and eventually halts. More formally it goes like this – given an n-state Turing Machine with a two symbol alphabet {0, 1}, what is the maximum number of 1's that the machine can print on an initially blank tape (filled with 0's) before halting?

Let's denote B(n) to be the number of 1s that the busy beaver managed to put on the tape. This function B(n) is called the busy beaver function and it is the solution to the busy beaver problem. It grows like this:

• B(1) = 1
• B(2) = 4
• B(3) = 6
• B(4) = 13
• B(5) = 4098

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Turing Machine for n-state busy beaver

Turing Machine for 1-state busy beaver:

• a0 -> h1r

Turing Machine for 2-state busy beaver:

• a0 -> b1r | a1 -> b1l
• b0 -> a1l | b1 -> h1r

Turing Machine for 3-state Busy Beaver:

• a0 -> b1r | a1 -> h1r
• b0 -> c0r | b1 -> b1r
• c0 -> c1l | c1 -> a1l

Turing Machine for 4-state Busy Beaver:

• a0 -> b1r | a1 -> b1l
• b0 -> a1l | b1 -> c0l
• c0 -> h1r | c1 -> d1l
• d0 -> d1r | d1 -> a0r

To run the following code just pass number of states as command line argument