S-adic 移位中的可识别性

Recognizability of morphisms

We investigate several questions related to the notion of recognizable morphism. The main result is a new proof of Mossé's theorem and actually of a generalization to non primitive morphisms due to Berthé et al. We actually prove the result of Berthé et al. for the most general class of morphisms, including ones with erasable letters. It is derived from a result concerning elementary morphisms for which we also provide a new proof. We also show how to decide whether an injective morphism is recognizable on the full shift for aperiodic points.

替换位移中的可判定问题

Decidable problems in substitution shifts

本文研究允许擦除态射的最一般替换位移的结构，并证明了非周期性、可识别性及不可约性等性质的可判定性。

Non-Archimedean dynamics of the complex shift

An (asynchronous) automaton transformation of one-sided infinite words over p-letter alphabet Fp = Z/pZ, where p is a prime, is a continuous transformation (w.r.t. the p-adic metric) of the ring of p-adic integers Zp. Moreover, an automaton mapping generates a non-Archimedean dynamical system on Zp. Measure-preservation and ergodicity (w.r.t. the Haar measure) of such dynamical systems play an important role in cryptography (e.g., in stream cyphers). The aim of this paper is to present a novel way of realizing a complex shift in p-adics. In particular, we introduce conditions on the Mahler exp…

Profinite automata

Many sequences of $p$-adic integers project modulo $p^α$ to $p$-automatic sequences for every $α\geq 0$. Examples include algebraic sequences of integers, which satisfy this property for every prime $p$, and some cocycle sequences, which we show satisfy this property for a fixed $p$. For such a sequence, we construct a profinite automaton that projects modulo $p^α$ to the automaton generating the projected sequence. In general, the profinite automaton has infinitely many states. Additionally, we consider the closure of the orbit, under the shift map, of the $p$-adic integer sequence, defining …