Zeno Machine

Zeno Machine

In mathematics and computer science, Zeno machines (abbreviated ZM, and also called Accelerated Turing machine, ATM) are a hypothetical computational model related to Turing machines that allows a countably infinite number of algorithmic steps to be performed in finite time. These machines are ruled out in most models of computation.

More formally, a Zeno machine is a Turing machine that takes 2-n units of time to perform its n-th step; thus, the first step takes 0.5 units of time, the second takes 0.25, the third 0.125 and so on, so that after one unit of time, an infinite number of steps will have been performed.

The idea of Zeno machines was first discussed by Hermann Weyl in 1927; they are named after the ancient Greek philosopher Zeno of Elea. Zeno machines play a crucial role in some theories. The theory of the Omega Point devised by physicist Frank J. Tipler, for instance, can only be valid if Zeno machines are possible.