Simulation of the Collatz 3x+1 function by Turing machines

Pascal Michel (1)

1 ELM - Équipe de Logique Mathématique

We give new Turing machines that simulate the iteration of the Collatz 3x+1 function. First, a never halting Turing machine with 3 states and 4 symbols, improving the known 3x5 and 4x4 Turing machines. Second, Turing machines that halt on the final loop, in the classes 3x10, 4x6, 5x4, and 13x2.

Mots clés: Collatz function; 3x+1 function; Turing machines

Domaines: Logique [math.LO]

Pascal Michel. Simulation of the Collatz 3x+1 function by Turing machines. 2014. ⟨hal-01067747⟩