The Undecidability of the Generalized Collatz Problem

The Collatz problem, widely known as the 3x + 1 problem, asks whether or not a certain simple iterative process halts on all inputs. We build on earlier work by J. H. Conway, and show that a natural generalization of the Collatz problem is recursively undecidable.

• Type: Conference
• Year: 2007
• Where: TAMC
• Authors: Stuart A. Kurtz, Janos Simon
• Keywords: Collatz Problem, Iterative Process Halts, Recursively Undecidable, TAMC 2007