It is shown that the problem of computing the Strahler number of a binary tree given as a term is complete for the circuit complexity class uniform $\mathsf{NC}^1$. For several variants, where the binary tree is given by a pointer structure or in a succinct form by a directed acyclic graph or a tree straight-line program, the complexity of computing the Strahler number is determined as well. We show that the problem of deciding whether a given context-free grammar in Chomsky normal form produces a derivation tree with a Strahler number of at least $k$ is $\mathsf{P}$-complete. If the derivation tree is restricted to be acyclic, the problem becomes $\mathsf{PSPACE}$-complete.

翻译：研究表明，以项形式给出的二叉树的Strahler数计算问题对电路复杂度类一致$\mathsf{NC}^1$是完全的。对于若干变体——其中二叉树通过指针结构给出，或通过有向无环图、树直线程序以简洁形式给出——计算Strahler数的复杂度同样被确定。我们证明，判定给定乔姆斯基范式下的上下文无关文法是否生成一棵Strahler数至少为$k$的推导树这一问题是$\mathsf{P}$-完全的。若该推导树被限制为无环，则该问题变为$\mathsf{PSPACE}$-完全的。