Automatic sequences are not suitable sequences for cryptographic applications since both their subword complexity and their expansion complexity are small, and their correlation measure of order 2 is large. These sequences are highly predictable despite having a large maximum order complexity. However, recent results show that polynomial subsequences of automatic sequences, such as the Thue–Morse sequence, are better candidates for pseudorandom sequences. A natural generalization of automatic sequences are morphic sequences, given by a fixed point of a prolongeable morphism that is not necessarily uniform. In this paper we prove a lower bound for the maximum order complexity of the sum of digits function in Zeckendorf base which is an example of a morphic sequence. We also prove that the polynomial subsequences of this sequence keep large maximum order complexity, such as the Thue–Morse sequence.

自动序列不适合密码应用的序列，因为它们的子字复杂度和扩展复杂度都很小，而且它们的 2 阶相关度量很大。尽管最大顺序复杂度很大，但这些序列是高度可预测的。然而，最近的结果表明自动序列的多项式子序列，例如 Thue-Morse 序列，是伪随机序列的更好候选者。自动序列的自然推广是态序列，由不一定一致的可延长态射的不动点给出。在本文中，我们证明了 Zeckendorf 基中数字之和函数的最大阶复杂度的下界，这是一个形态序列的例子。