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Theory and Applications of Models of Computation

Volume 4484 of the series Lecture Notes in Computer Science pp 542-553

The Undecidability of the Generalized Collatz Problem

  • Stuart A. KurtzAffiliated withDepartment of Computer Science, The University of Chicago
  • , Janos SimonAffiliated withDepartment of Computer Science, The University of Chicago

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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 \({\it \Pi}^0_2\) complete.