An S-adic characterization of minimal subshifts with first difference of complexity 1 ≤ p(n + 1) − p(n) ≤ 2 S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is S-adic with Card(S) ≤ 3 27. In this paper, we improve this result by giving an S-adic characterization of these subshifts with a set S of 5 morphisms, solving by this way the S-adic conjecture for this particular case.

Source : oai:HAL:hal-01179422v1

Volume: Vol. 16 no. 1 (in progress)

Section: Automata, Logic and Semantics

Published on: May 4, 2014

Submitted on: June 3, 2013

Keywords: special factor,factor complexity,S-adic conjecture,Rauzy graph,S-adic subshift,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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