Confusion of memory

It is a truism that for a machine to have a useful access to memory or workspace, it must “know” where its input ends and its working memory begins. Most machine models separate input from memory explicitly, in one way or another. We are interested here in computational models which do not separate input from working memory. We study the situation on deterministic single-queue machines working on a two symbol alphabet. We establish a negative result about such machines: they cannot compute the length of their input. This confirms the intuition that such machines are “unable to tell” where on the queue the input ends and the memory begins. On the positive side, we note that there are some interesting things that one can do with such queue machines: their halting problem is undecidable, there are self-replicating machines, and there are recognizable languages outside of the control hierarchy.