The undecidability of the generalized Collatz problem

Authors:
Stuart A. Kurtz;Janos Simon
Affiliations:
Department of Computer Science, The University of Chicago;Department of Computer Science, The University of Chicago
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

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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 Π20 complete.