Information Processing Letters 107 (2008) 114–119 www.elsevier.com/locate/ipl Confusion of memory Lawrence S. Moss Department of Mathematics, Indiana University, Bloomington, IN 47405, USA Received 21 November 2007; received in revised form 11 February 2008 Available online 19 February 2008 Communicated by L. Boasson Abstract 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.  2008 Elsevier B.V. All rights reserved. Keywords: Theory of computation; Models of computation; Formal languages This paper is a comment on input vs. memory/ workspace as they appear in machine models of com- putation. Usually, these are kept separate, using extra symbols, different tapes or registers, or other devices. Often in presentations this is done tacitly: “obviously” a machine would need to treat its input differently from the rest of its working space. In this note, we wish to treat the matter in a little more detail, by proposing a simple computational set- ting where working memory is not clearly separate from input. One way to do this would be to look at Turing machines whose input might contain the blank symbol. Our proposal goes in a different direction, based on reg- ister machines (see Shepherdson and Sturgis [6] or other E-mail address: lsm@cs.indiana.edu. sources such as Enderton [1]). Normally, a register ma- chine has many registers and works on numbers in unary notation, or else on words from some alphabet. We wish to consider only one register, and to make our point we must consider an alphabet A of at least two symbols. We take A to have exactly two symbols, 1 and #. The input and workspace on such a machine comes in the form of a FIFO queue. The queue is unbounded, and all reading comes from one side and all writing to the other. There is no special “end of input” symbol, and there also are no other registers. So any writing that goes on the end of the queue will be conflated with the input. The machine itself may be taken as a finite automa- ton controlling the queue. Alternatively, one can dis- pense with states and transition rules in favor of pro- grams. Some of our results are more easily stated this way, and so we adopt a fixed language for programs. 0020-0190/$ – see front matter  2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ipl.2008.02.002