Different number for Turing machine states after running laconic_to_2s_tm_compiler.py

[skoestlmeier]

The original file ./src/tm/tm2/tm2_files/goldbach.tm2 for the Goldbach Turing machine has 4,888 states (see line 1 of the file) which is also declared in the research paper "A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory".

If i run python laconic_to_2s_tm_compiler.py goldbach to your original goldbach.lac file, the new created file goldbach.tm2 has only 4,876 states.

Running diff -u goldbach_original.tm2 goldbach.tm2 > goldbach_difference.txt reveals differences not only in the number of states but also in transitions. The file goldbach_difference.txt is accesible here and the goldbach.tm2 after running laconic_to_2s_tm_compiler.py here.

I am running my code on a MacBook Pro with Apple M1 Pro chip:
System Version: macOS 14.4.1 (23E224)
Kernel Version: Darwin 23.4.0
System Firmware Version: 10151.101.3
OS Loader Version: 10151.101.3

Why is there a difference in the number of Turing machine states and does this affect the behavior of the Turing machines?