Talk:Tag system

message: The cyclic tag system does not properly emulate the halt. It treats H just like any other symbol.
It might be better to change the H to a neutral letter like c.
GuenterRote (talk) 07:36, 9 August 2023 (UTC)
thread_title:  Example of cyclic tag system simulation 

message: Current version of the article does not explicitly state what is the role of m number. Only through the examples it is possible to guess its role.  — Preceding unsigned comment added by 89.69.161.56 (talk) 13:18, 26 February 2012 (UTC)
thread_title:  Deletion number 

message: Wikipedia also has an article on Post machines, which seem virtually identical to Tag systems, except for the way they are described.  It would probably be a good idea  to merge/link these two articles somehow. --Chris Pressey 17:20, 16 July 2005 (UTC)
replies: text: I finally got around to incorporating a brief abstract machine description into Tag system, and have now redirected Post machine to this article.--r.e.s. (Talk) 21:38, 28 December 2005 (UTC)
thread_title:  Merging "Post machine" page into this one 

message: I hope JohnnyNyquist will not be too annoyed by my editing -- it seemed a good idea to make the description of cyclic tag systems use more of Rogozhin's terminology for tag systems. Also, although I tried to make the emulation section as brief as I could, it still seems a bit bulky -- but the example seems worth the space, imo.  
--r.e.s. (Talk) 11:17, 26 December 2005 (UTC)
thread_title:  Rewording to better integrate cyclic tag systems 

message: Viral tagging ftw!
I would like to propose a new spin on the old TAG SYSTEM.  I call it VIRAL TAGGING.  The basics of it are on my website which is redonkulicity.com/theory.html
I don't know how to use wikipedia to add articles, but would LOVE anyone to create a stub linked to the TAG SYSTEM, and VIRAL kinds of categories, or even understand what I'm saying and put that on the page.
The most specific and useful type of VIRAL TAGGING would be WEIGHTED ITERATIVE VIRAL TAGGING.  And the coolest thing I could think of at the moment would be a webcrawler designed as a WIVT machine. —The preceding unsigned comment was added by Wubitog (talk • contribs) 16:21, 30 January 2007 (UTC)
thread_title:  Weighted, Viral, Population, Tagging, Mechanisms  

message: Does anyone out there know the status of the problem (see the annotation of the Minsky 1967 reference) w.r.t. undedicability and intractability? This fact should be prominent in the article. . My only reference to the "tag" problem is Minsky 1967, i.e. pretty ancient. 
:I think you're referring to this ad hoc test-case from Post 1943 (which is somewhat misstated by Minsky): Given the 3-tag system with production rules (0 -> 00, 1 -> 1101) on alphabet {0,1}, determine whether iteration of the tag operation eventually terminates in an empty string when started with an arbitrary initial word. (Where, in keeping with Post, the tag operation is as I paraphrase it in the Historical note section of the article, not as Minsky misstates it.) AFAIK, it's still an open question whether this is an unsolvable halting problem, in contrast to certain known 2-tag systems whose halting problem is provably unsolvable. --r.e.s. 22:58, 7 October 2007 (UTC)
replies: text: Although I agree the test-case might deserve a brief mention merely because it has resisted attempts to prove anything about its solvability, it certainly should not be more prominent than the following point already in the article (in the Definition section): "For each m > 1, the set of m-tag systems is Turing-complete."  E.g., we know how to convert any Turing machine into an equivalent 2-tag system. (If you're curious, you can find all the gory details of converting any binary TM to a 2-tag system here, which is a subsection of a webpage about Bitwise Cyclic Tag.) Maybe these points about Turing completeness (which to my mind are the really important ones) should be made more prominent. --r.e.s. 22:58, 7 October 2007 (UTC)

text: In my opinion, about all that can be said concerning the test-case in question is that, so far, everyone has found it to be "intractable" -- it might, or might not, actually be an unsolvable halting problem. I don't think speculations or original work on suspected possible "connections" to Collatz should be discussed in the article. --r.e.s. 22:58, 7 October 2007 (UTC)
replies: text: No, no... I totally agree with you, such speculations would have no place here unless they were corroborated in the literature. I was just hoping it might trigger in someone's mind an association to other work, seemingly unrelated. Early this past winter I spent about 3 months fiddling with the Collatz Conjecture and arrived at a dead end. I was more interested in a possible example for proof of impossibility. Thanks, Bill wvbaileyWvbailey 03:00, 8 October 2007 (UTC)

text: Following up a bit on the connection between the Collatz problem and tag systems ... An online article by L. De Mol points out that the extremely simple 2-tag system (a -> cb, b -> aaa, c -> a) computes the Collatz sequences for the Collatz function in the form C(n) = (if n is even then n/2 else (3n+1)/2).  In this tag system, a positive integer n is represented by the word aa...a with n a's.  If the author had used Post's original definition (i.e. halting only on the empty word), the tag system would never halt, and the endless cycle (... -> 1 -> 2 -> 1 -> ...) would be faithfully simulated; however, since she uses the alternative halting criterion, the tag system halts on 1 (i.e. when the word has fewer than 2 letters), which in a way is more convenient.--r.e.s. 06:22, 10 October 2007 (UTC)
replies: text: The above is very interesting. And exciting: I'm glad to see some sharp minds tackling the problem from this angle. The mathematicians I was corresponding with winter were unaware of this "tag" business, and Minsky's 1961 paper "Recrusive Unsolvability of Post's Problem of "tag" and other Topics in Theory of Turing machines" in particular. I'll enter this paper into the article's bibliography. Thanks, Bill Wvbailey 15:42, 10 October 2007 (UTC)

text: I've expanded the Definition section of this article to clarify the types of tag system that don't use a halting symbol, and added a worked example of De Mol's 2-tag system for Collatz sequences (and of course cited her article in References). I also slightly expanded the Turing-completeness portion as a separate section. --r.e.s. 17:50, 10 October 2007 (UTC)

text: As De Mol's article points out, it's notable that the "smallest" known universal tag system has an alphabet of around 500 symbols, and a value of (deletion_number * number_of_symbols) that's correspondingly huge, whereas one might expect universality to crop up in tag systems not much larger (if at all) than the ones capable of computing Collatz sequences — like the present example, where that product is a mere 6.  As an aside, FWIW, I've managed to slightly reduce the size of the monster universal tag system cited by De Mol, by removing redundancies in the Cocke-Minsky machine used to simulate the UTM (and have also extended the formalism to simulate any given TM — not just 2-symbol ones — by a tag system); but as it's my "original research", and not peer reviewed, I can only point any interested readers to it by this link. --r.e.s. (talk) 03:17, 20 November 2007 (UTC)

text: Alright, I'm moving it to Talk:Counter machine and will try not to butcher it in the process. --r.e.s. (talk) 01:50, 23 November 2007 (UTC)

text: What you've created is a nice programming language for controlling the read/write heads of the machine in a way that allows it to operate much differently than a tag machine (which has only one state). Your machine, with arbitrarily many states (instructions in a program) can probably simulate binary k-tag for any k, but it can do many other things a k-tag machine cannot do — most importantly, it can freely write any word at any time, and isn't constrained to always perform just the single composite operation of a tag system (i.e., read one symbol and advance the tape a fixed number k of squares at the read-head when appropriate, always writing just the fixed word specified for the symbol that was read, etc.). --r.e.s. (talk) 20:40, 24 November 2007 (UTC)

text: { LA, LB, PB(symbol), Js(symbol,address), J(address), halt }.
This simulator does only one symbol-compare at a time. So there are three of them, instructions #1, #2, #3, and three "state executions" as indicated by the colors (the "operations" are assumed to be occurring on the transitions but each is shown as a sequence of instructions) . Thus "blue" prints "bc" and moves two symbols right into the string, "purple" prints "a" and moves two symbols into the string, and "orange" prints "aaa" and moves two symbols into the string. 
Instruction #:               	1 	2 	3 	4 	5 	6 	7 	8 	9 	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
Instruction:                 	Js	Js	Js	PB	LB	PB	LB	LA	LA	J 	PB	LB	LA	LA	J 	PB	LB	PB	LB	PB	LB	LA	LA	J
Print symbol:                	  	  	  	b 	  	c 	  	  	  	  	a 	  	  	  	  	a 	  	a 	  	a 	  	  	  	
Test symbol:                 	a 	b 	c 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	
If symbol-match then jump to:	4 	11	16	  	  	  	  	  	  	1 	  	  	  	  	1 	  	  	  	  	  	  	  	  	1
My working through this and your pointing out that the tag "machine" is a one-state machine (with e.g. three transitions for the Collatz sequence) helped me understand this a lot.
I'd suggest that this state-machine aspect of the tag machine become more prominent in the article. I will mull over how to do a state-machine drawing of the Collatz machine; the only "complication" is that a whole lot of stuff happens on a transition. This is a quibble with "true" Turing machines too, that "shift" and "print" or vice versa, are not atomic (i.e. they occur in a sequence. And printing a symbol string is even less a single state if we assume one symbol per square of tape). So, I suppose we might think of the above little machine's actions as representing an "atomization" of the (one-state) tag machine's various actions in a state-transition. Bill Wvbailey (talk) 23:04, 24 November 2007 (UTC)

text: I'm responding here to a question you asked over in Talk:Counter machines: "can a tag machine calculate 2N given N encoded as unary on its tape??".  For machines that correspond to Post's tag systems (i.e. not multi-state machines), istm that the answer might well be "no", where the "unary" encoding of N would be a same-letter string of length N*k for a k-tag system. (But then, I don't claim to be adept at even elementary number theory, which is what these systems inherently involve — Post called it "the intrusion of number theory".) However, I think it's worth noting that even the simple 1-tag system (a -> aa) computes the function n → 2n (n ≥ 0) starting with the initial word 'a'. Just as Turing's original computing machines compute the nth digit of a (computable) real number as the nth figure written on the tape — without ever halting — here the nth term of the infinite sequence 20, 21, 22 ... is the nth term produced by the tag system, coded in "unary" as a string of 'a's.--r.e.s. (talk) 01:35, 29 November 2007 (UTC)

text: No, I'm unaware of such a tag system, which is exactly why I replied 'istm that the answer might well be "no"' to your question above. --r.e.s. (talk) 23:12, 29 November 2007 (UTC)
thread_title:  Intractability? proof of impossibility or undecidability? 

message: When it says 2-tag system, what does the 2 refer to? It seems to be the halting length, but the article doesn't seem to explicitly say, and I'm new to this topic, so I'm not positive. — Olathe (talk) 01:42, 30 October 2012 (UTC)
thread_title:  n-tag definition 

message: We should clearly disambiguate this from tag systems in the non-mathematical sense.  
For example https://news.ycombinator.com/item?id=35597934 (https://buttondown.email/hillelwayne/archive/tag-systems/) is not related. 2403:6200:8851:D9B4:4843:9546:EBBC:EB0A (talk) 11:20, 14 July 2023 (UTC)
thread_title:  change this to https://en.m.wikipedia.org/wiki/Tag_system_(mathematics)