0

So in a book that I'm reading it says that we can convert any given Turing machine to a standard turing machine with only 6 states

furthermore we can convert any given to a turing machine with only 3 states given we have no limitation on which version of turing machine we use(multi tape, non deterministic, etc so its not a standard turing machine anymore) and obviously both the original turing machine and the converted one have the same functionality(accept the same language)

i asked this here before but no one was able to give a proof of this, and i do not understand it either

so what's this statement based on? i tried searching the web but there was literally 0 article about this.

I think this is done the same way we can reduce any PDA to a PDA with only 3 states, but i dont know the prove of that one either, i just know its true

John P
  • 750
  • 4
  • 18
  • 1
    I asked this here before. You should include a link to your earlier question. – Yuval Filmus Apr 14 '18 at 19:15
  • 1
    Here is the earlier question: https://cs.stackexchange.com/questions/89765/can-we-convert-any-given-turing-machine-to-a-turing-machine-with-only-2-states. – Yuval Filmus Apr 14 '18 at 20:34
  • See also https://cs.stackexchange.com/questions/43517/what-is-the-limit-for-turing-machines-with-2-states-and-3-symbols-that-halt. – Yuval Filmus Apr 14 '18 at 20:35
  • What's the difference from the old question? – xskxzr Apr 15 '18 at 03:06
  • @xskxzr in the old one i said 2 states but that was not right, the correct minimum is 3, and i have not found the prove yet ( but i think reducing the number of states is done the same way that we can reduce any given PDA to a PDA with only 2 states, but i dont know the prove of that one either) all of these are side notes in the book without any prove – John P Apr 15 '18 at 03:39
  • It would likely be helpful if you cited the book. – Derek Elkins left SE Apr 15 '18 at 09:31
  • @DerekElkins Its a translation of peter linz - automata in the turing machine chapter, not sure if these side notes are in the original book or not – John P Apr 15 '18 at 11:23

0 Answers0