在无限树上分配标签
Distributing Labels on Infinite Trees
摘要：
Sturmian字是无限的二进制字，有许多等价的定义：它们在所有非周期序列中具有最小的因子复杂度;它们是平衡序列（标签0和1尽可能均匀分布），它们可以使用机械定义来构造。所有这些性质使他们成为两个处理器上的调度问题的极值点很好的候选人。在本文中，我们考虑的问题，推广Sturmian词树。问题是将标签0和1均匀分布在无限树上。我们表明，（强）平衡树存在，也可以使用一个机械的过程，只要树是不合理的。这样的树也有一个最小的因子复杂度。因此，他们带来了希望，极值调度性能的Sturmian字可以扩展到这样的树，至少部分。通过一个这样的示例来说明这样的可能的扩展。
英文摘要：
Sturmian words are infinite binary words with many equivalent definitions: They have a minimal factor complexity among all aperiodic sequences; they are balanced sequences (the labels 0 and 1 are as evenly distributed as possible) and they can be constructed using a mechanical definition. All this properties make them good candidates for being extremal points in scheduling problems over two processors. In this paper, we consider the problem of generalizing Sturmian words to trees. The problem is to evenly distribute labels 0 and 1 over infinite trees. We show that (strongly) balanced trees exist and can also be constructed using a mechanical process as long as the tree is irrational. Such trees also have a minimal factor complexity. Therefore they bring the hope that extremal scheduling properties of Sturmian words can be extended to such trees, as least partially. Such possible extensions are illustrated by one such example.
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