Affiliations: Università di Verona, Dipartimento di
Informatica, Ca' Vignal 2, Strada Le Grazie, 15-37134 Verona, Italy.
giuseppe.scollo@univr.it
Note: [] Address for correspondence: Università di Verona,
Dipartimento di Informatica, Ca' Vignal 2, Strada Le Grazie, 15-37134 Verona,
Italy
Abstract: The Collatz problem is comprised of two distinct, separate
questions: existence of eventually periodic Collatz reductions with a
nontrivial period, and existence of period-free Collatz reductions. This paper
introduces a few distinct, related formalizations of the Collatz dynamics as
term rewriting systems, using elementary concepts from the theory of state
transition dynamics. Some of the subject systems act on finite terms, whereas
others rewrite terms that are endowed with a countable, recursively defined
structure. The latter presents a convenient framework for the investigation of
extensions of the Collatz dynamics to dense systems.
Keywords: state transition dynamics, attractor, periodicity, quasiperiodicity, infinitary rewriting
