16 citations · 24 across the 5 of their papers we have counts for
Showing math.LOShow all
3 papers · 1 filter
math.LO2014★ 5 cited
Simulation of the Collatz 3x+1 function by Turing machines
Pascal Michel
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…
math.LO2013★ 3 cited
Problems in number theory from busy beaver competition
Pascal Michel
By introducing the busy beaver competition of Turing machines, in 1962, Rado defined noncomputable functions on positive integers. The study of these functions and variants leads t…
math.LO2009★ 16 cited
The Busy Beaver Competition: a historical survey
Pascal Michel
Tibor Rado defined the Busy Beaver Competition in 1962. He used Turing machines to give explicit definitions for some functions that are not computable and grow faster than any com…