I have searched the web for the transition diagram of a universal Turing machine without luck. Is anyone aware of such a diagram?

I need this as a reference, so preferably a book or a published article. I don't want anything strange, just a standard Turing Machine with one tape that computes the Universal Turing Machine. The tape will contain a Turing machine and an input string. The rest of the tape is filled with blank.

I would prefer historic references.

  • $\begingroup$ Maybe this Wolfram demonstration is close to what you are looking for: demonstrations.wolfram.com/… . I think a similar style was used in Wolfram's book 'A new kind of science'. $\endgroup$ Commented Feb 17, 2012 at 8:55
  • $\begingroup$ According to the information found on this web page (rdrop.com/~half/General/UTM/index.html), the complete description of an UTM is contained in one of the first editions of the book: "Formal Languages and Their Relation to Automata" by Hopcroft & Ullman. Perhaps someone can search the book in its library and see if the information is correct (... and scan the pages with the UTM). $\endgroup$ Commented Feb 17, 2012 at 11:57

2 Answers 2


I found the book:

 author = {Hopcroft, John E. and Ullman, Jeffrey D.},
 title = {Formal languages and their relation to automata},
 year = {1969},
 publisher = {Addison-Wesley Longman Publishing Co., Inc.},
 address = {Boston, MA, USA},

and this is a link to a pdf scan of the UM description (7 pages).


Here are some references:

Also Odifreddi writes ["Classical Recursion Theory", vol I, p. 133]:

"..., and explicit constructions of universal Turing machines are in Turing [1936], Wang [1957a] and in many textbooks, e.g. Hermes [1965], Minsky [1967], Arbib [1969], Hopcroft and Ullman [1979]. More information on the topic is in Davis [1956], [1957], Shannon [1956], Rogers [1967] and Priese [1979]."


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