Skip to main content Accessibility help

Recursive Unsolvability of a problem of Thue

  • Emil L. Post (a1)


Alonzo Church suggested to the writer that a certain problem of Thue [6] might be proved unsolvable by the methods of [5]. We proceed to prove the problem recursively unsolvable, that is, unsolvable in the sense of Church [1], but by a method meeting the special needs of the problem.

Thue's (general) problem is the following. Given a finite set of symbols α1, α2, …, αμ, we consider arbitrary strings (Zeichenreihen) on those symbols, that is, rows of symbols each of which is in the given set. Null strings are included.



Hide All
[1]Church, Alonzo, An unsolvable problem of elementary number theory, American journal of mathematics, vol. 58 (1936), pp. 345363.
[2]Post, Emil L., Finite combinatory processes—formulation 1, this Journal, vol. 1 (1936), pp. 103105.
[3]Post, Emil L., Formal reductions of the general combinatorial decision problem, American journal of mathematics, vol. 65 (1943), pp. 197215.
[4]Post, Emil L., Recursively enumerable sets of positive integers and their decision problems, Bulletin of the American Mathematical Society, vol. 50 (1944), pp. 284316.
[5]Post, Emil L., A variant of a recursively unsolvable problem, Bulletin of the American Mathematical Society, vol. 52 (1946), pp. 264268.
[6]Thue, Axel, Probleme über Veränderungen von Zeichenreihen nach gegebenen Regeln, Skrifter utgit av Videnskapsselskapet i Kristiania, I. Matematisk-naturvidenskabelig Klasse 1914, no. 10 (1914), 34 pp.
[7]Turing, A. M., On computable numbers, with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, ser. 2 vol. 42 (1937), pp. 230265.
[8]Turing, A. M., Computability and λ-definability, this Journal, vol. 2 (1937), pp. 153163.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed