The Undecidability of the Generalized Collatz Problem

  • Stuart A. Kurtz
  • Janos Simon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)


The Collatz problem, widely known as the 3x + 1 problem, asks whether or not a certain simple iterative process halts on all inputs. In this paper, we build on work of J. H. Conway to show that a natural generalization of the Collatz problem is \({\it \Pi}^0_2\) complete.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Stuart A. Kurtz
    • 1
  • Janos Simon
    • 1
  1. 1.Department of Computer Science, The University of Chicago 

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