Note that this result does not directly follow from the well-known total function problem (Does a given machine halt for every input?
), since the latter problem concerns only valid computations (starting with an initial configuration).
The variant in which only finite configurations are considered is also undecidable, as proved by Herman,[2] who calls it ''the uniform halting problem''.
The problem can naturally be rephrased for any computational model in which there are notions of "configuration" and "transition".
A member of the model will be mortal if there is no configuration that leads to an infinite chain of transitions.