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Does anyone know whether universal queue automata have ever been considered, and, as for Universal Turing Machines, some "small" universal queue automata are known?

Sophie Pinchinat
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    https://cs.stackexchange.com/questions/21460/prove-queue-automaton-is-equivalent-to-turing-machine What do you mean by "considered"? What examples are you looking for? – Evil Oct 12 '17 at 20:04
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    Have they ever been considered? You've considered them, so now they have. What would you like to know about them? I guess that the reduction showing equivalence of TM's and queue automata immediately gives examples of universal queue automata; simply take any universal TM, and apply that reduction to get a queue automaton that is (presumably; you should check this) universal. – D.W. Oct 12 '17 at 20:43
  • Dear colleagues (@Evil and @D.W.), "considered" in a scientific context should be interpreted as "studied", sorry for not being clear. Now I am looking for small ones, and meanwhile I found a very close model where small machines have been exhibited: Alhazov, A., Kudlek, M., & Rogozhin, Y. (2002). Nine universal circular Post machines. Computer Science Journal of Moldova, 10(3), 30. – Sophie Pinchinat Oct 14 '17 at 06:11

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Well, a very similar concept, called Tagsystems is an early universal model developed by Post. Here is the description from wikipedia:

A tag system is a deterministic computational model published by Emil Leon Post in 1943 as a simple form of a Post canonical system. A tag system may also be viewed as an abstract machine, called a Post tag machine (not to be confused with Post-Turing machines)—briefly, a finite state machine whose only tape is a FIFO queue of unbounded length, such that in each transition the machine reads the symbol at the head of the queue, deletes a constant number of symbols from the head, and appends to the tail a symbol-string that depends solely on the first symbol read in this transition.

It is explained in the introductory part of a paper by Woods and Neary for FOCS 2006 that small universal TM's are actually built from small universal Tag-systems. Hence there is a big competition in finding small Tag-systems.

Hendrik Jan
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