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Issue title: Contagious Creativity – In Honor of the 80th Birthday of Professor Solomon Marcus
Article type: Research Article
Authors: Scollo, Giuseppe
Affiliations: Università di Verona, Dipartimento di Informatica, Ca' Vignal 2, Strada Le Grazie, 15-37134 Verona, Italy. [email protected]
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
Journal: Fundamenta Informaticae, vol. 64, no. 1-4, pp. 405-416, 2005
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