论文标题
PISOT常规序列的鲁棒性
Robustness of Pisot-regular sequences
论文作者
论文摘要
我们考虑基于$ d $ -tuple $ \ mathbf {u} =（u_1，\ ldots，u_d）$的整数序列，我们定义$（\ mathbf {u}，\ mathbb {k}半度。我们表明，对于Pisot Numeration Systems的任何$ D $ -Tuple $ \ Mathbf {U} $，以及任何交换性的$ \ Mathbb {k} $，此定义不取决于$ \ Mathbf {u} $的贪婪。该证明具有建设性，是基于以下事实：标准化可以通过$ 2D $ tape有限的自动机实现。特别是，我们使用一个临时操作，混合$ 2D $ -TAPE自动机和$ \ Mathbb {K} $ - 自动机，以获得新的$ \ Mathbb {K} $ - automaton。
We consider numeration systems based on a $d$-tuple $\mathbf{U}=(U_1,\ldots,U_d)$ of sequences of integers and we define $(\mathbf{U},\mathbb{K})$-regular sequences through $\mathbb{K}$-recognizable formal series, where $\mathbb{K}$ is any semiring. We show that, for any $d$-tuple $\mathbf{U}$ of Pisot numeration systems and any commutative semiring $\mathbb{K}$, this definition does not depend on the greediness of the $\mathbf{U}$-representations of integers. The proof is constructive and is based on the fact that the normalization is realizable by a $2d$-tape finite automaton. In particular, we use an ad hoc operation mixing a $2d$-tape automaton and a $\mathbb{K}$-automaton in order to obtain a new $\mathbb{K}$-automaton.
