The Undecidability of the Generalized Collatz Problem

  • Stuart A. Kurtz
  • Janos Simon
Conference paper

DOI: 10.1007/978-3-540-72504-6_49

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)
Cite this paper as:
Kurtz S.A., Simon J. (2007) The Undecidability of the Generalized Collatz Problem. In: Cai JY., Cooper S.B., Zhu H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg

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.

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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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