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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)

Abstract

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.

Keywords

Partial Function FracTran Program Congruence Class Universal Totality Counter Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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