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.
|Titolo:||ω-rewriting the Collatz problem|
|Data di pubblicazione:||2005|
|Citazione:||ω-rewriting the Collatz problem / SCOLLO G. - In: FUNDAMENTA INFORMATICAE. - ISSN 0169-2968. - 64:1-4(2005), pp. 405-416.|
|Appare nelle tipologie:||1.1 Articolo in rivista|