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

Abstract : 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.
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Preprints, Working Papers, ...
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Contributor : Pascal Michel Connect in order to contact the contributor
Submitted on : Wednesday, September 24, 2014 - 8:50:08 AM
Last modification on : Friday, March 27, 2020 - 3:01:26 AM
Long-term archiving on: : Thursday, December 25, 2014 - 10:21:18 AM


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  • HAL Id : hal-01067747, version 1
  • ARXIV : 1409.7322



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



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