Talk:Turing machine/Archive 1

message: This page really needs a diagram. Even a simple one would do. I'll take care of this in a while if no one else gets to it. Deco 00:58, 2 Oct 2004 (UTC)
replies: text: I have one at , although it's not particularly attractive.  If you do want to use it, I hereby release the illustration under the terms of the GFDL. -- Dominus 14:10, 2 Nov 2004 (UTC)
replies: text: I like it, but I'd prefer something that shows that the tape is semi-infinite and evokes that finiteness of the control. I'm thinking of adding in the "toy train" metaphor somewhere, and a diagram to go with that. (The train metaphor is that the read/write head is represented by a toy train on a track that extends forever in one direction, and it decides without any outside control which way to go based on the character under it. Less clear, though, is how a train writes characters on the track.) Deco 23:52, 2 Nov 2004 (UTC)
replies: text: According to the wikipedia article, the tape is infinite in both directions. -- Dominus 14:08, 3 Nov 2004 (UTC)
replies: text: You're right. I usually see it treated with a semi-infinite tape, as in Sipser, but admittedly this complicates the mechanics a bit (you need to say what happens when it moves left from the leftmost cell). On the other hand it helps sometimes to be able to speak of the "beginning" of the tape, but you might as well label them with integers and call the cell labelled zero the "origin" of the tape. I'm unsure which is better for education. Deco 18:17, 3 Nov 2004 (UTC)
thread_title:  Diagram 

message: I know Turing machines were used a lot in military and industrial sector applications before computers made their way through as the mainly used calculating machines;  but were Turing machines ever produced by any company on a wider market for small-business clients?
: Turing machines are a purely theoretical concept, not real machines. There were different calculating machines before the computer used by military as well as by bigger businesses. -- till we ☼☽ | Talk 08:55, 29 Nov 2004 (UTC)
thread_title:  Were the actual machines ever widely produced pre-computer era? 

message: Im curious about the use of the term "state" in this document. 
It seems to me that two seperate concepts of state are referred to in the document without distinguishing them.  Consider that in the "informal description" it keeps the concept of state and memory distinct:
"
1. A tape which is divided into cells, one next to the other. Each cell contains a symbol from some finite alphabet. The alphabet contains a special blank symbol (here written as '0') and one or more other symbols. The tape is assumed to be arbitrarily extendible to the left and to the right, i.e., the Turing machine is always supplied with as much tape as it needs for its computation. Cells that have not been written to before are assumed to be filled with the blank symbol. 
....
3. A state register that stores the state of the Turing machine. The number of different states is always finite and there is one special start state with which the state register is initialized.
"
However later on in the section "Comparison with real machines" a different "state" is discussed (albeit implicitly): "What is missed in this statement is that almost any particular program running on a particular machine and given a finite amount of input is in fact nothing but a deterministic finite automaton, since the machine it runs on can only be in finitely many states." 
The problem here is that in the first case "state" is held to be distinct from memory. In the second case memory and state are merged. The truth is that a "real computer" is much closer to a turing machine (with memory distinct from state) than it is to a DFA (with no memory outside of state).
:I agree with you up to this last sentence. Two different senses of "state" have been used, both of which are common and established in their own areas, and this is potentially confusing. But "state" as the word is used in talking about real computers definitely includes the contents of memory; and "state" as the word is used in talking about Turing machines does not map neatly onto any feature of real computers. So I don't think it would be clear to say "The truth is that a 'real computer' has memory distinct from its state."
:In a related issue, after mapping DFAs to Turing machines (where the "state" is not the main form of storage), and then mapping Turing machines to real computers, we are then asked to map real computers back onto DFAs. But this time, we're using "state" in the sense of the complete configuration of a computer's memory, registers, hard drives, and whatever...and mapping that back onto the DFA sense of "state". Meaning we end up with a DFA with two-to-the-trillionth-power different states or something, as you've mentioned below, and it seems like a technicality to call that "finite". However, this is indeed what people mean in saying a real computer is only as powerful as a DFA.
It seems to me that this mixed use in the discussion of any form of finite state automata is extremely confusing. Either a turing machine has infinite states,
:(in the sense of "state" used in talking about real computers, it does...)
or a "real computer" is a turing machine with restricted memory. If we accept that a "real computer" is equivelent to a DFA then we shouldnt discuss Turing machines as though they were finite state machines. Also in todays market of mass storage devices and backup tapes IMO a modern computer has essentially infinte resources to work with. After all we could keep adding new harddrives ad nauseum. 
:This is true and I've added it to the article.
I also think that the merging of state and memory is problematic as it implies that the state of the machine is a holistic one comprising of the combined state of every mass storage device and memory address that the computer can access. Since a single byte of RAM implies 256 distinct states a computer with a few terabytes of mass storage available and a few gigabytes of memory would have more states than there are atoms in the universe. Add a network connection and the number of states that the machine can be in just explodes.
:Right. And that is what they mean. It's a huge number but it is still finite and that's their point. I've tried to address the distance between that and any practical limitations, in my addition to the article.
Maybe this is just the ramblings of a confused man, but personally i feel that there is a problem here. Some areas where it gets confusing is that in other documents we see that one requires a turing machine to process a type 0 language and that DFA's and NFA's can only handle a type 3 language. However if a "real computer" is really a DFA then how can it process a type 0 language like C which requires handling recursive constructs (which we know a DFA cannot.)
:A real computer can't necessarily process a fifty petabyte C program. Not that there is any such thing AFAIK.
:DanielCristofani 10:04, 16 May 2005 (UTC)
thread_title:  The meaning of "state", and computers as DFAs 

message: The edit at 05:45, 30 July 2005 by 202.56.193.222 just removed the artist's conception of a turing machine without any reason given. Is there anything wrong with it? Does anyone object if I put the picture back? --Lemontea 13:34, 30 July 2005 (UTC)
replies: text: I posted to the anon user's empty talk page asking why he deleted the image. Let's wait a day and if we don't get a response, reintroduce it. Rmrfstar 14:20, 30 July 2005 (UTC)
replies: text:  I have just reintroduced the image into the article because we have heard no justification for its removal and some users have requested its reimplementation. -- Rmrfstar 21:25, 31 July 2005 (UTC)
thread_title:  Deleted picture? 

message: Turing did not describe a stack of sheets of paper in his article. What he said was:
 Computing is normally done by writing certain symbols on paper. We may suppose this paper is divided into squares like a child's arithmetic book. In elementary arithmetic the two-dimensional character of the paper is sometimes used. But such a use is always avoidable, and I think that it will be agreed that the two-dimensional character of paper is no essential of computation. I assume then that the computation is carried out on one-dimensional paper, i.e. on a tape divided into squares.
Further, the first paragraph of the Wikipedia article made it sound like "the Turing machine was developed later from Turing's article, which only talked about pen-and-paper computation"; where in fact Turing's article is all about Turing machines and only mentions pen-and-paper computation as an analogy in order to try to convince people that a Turing machine can do anything that can be done with pen and paper.
Rewriting the first paragraph was a tricky balancing act, because of the nature of Turing machines; they have an unusual position, since
1. it was necessary that it be obviously possible to build them, since they are meant as an example of what can in fact be computed mechanically; but
2. it was not important to actually build them, nor did anyone at the time think it would be a good idea to do so.
Physical artifacts which are designed to remain merely possible are comparatively rare; I hope the present wording makes their status clear.
I decided not to put the title of Turing's paper in the first paragraph since it's long and non-crucial.
I made some other tweaks for style and/or accuracy at the same time; discussion is welcome. DanielCristofani 06:01, 17 December 2005 (UTC)
thread_title:  Notes on changes, December 2005 

message: Substituted at 20:55, 4 May 2016 (UTC)
thread_title: Assessment comment