On the complexity of computing Strahler numbers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912782045151232 |
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| author | Ganardi, Moses Lohrey, Markus |
| author_facet | Ganardi, Moses Lohrey, Markus |
| contents | 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. The problem, whether a given context-free grammar in Chomsky normal form produces a derivation tree (resp., an acyclic derivation tree), whose Strahler number is at least a given number $k$ is shown to be P-complete (resp., PSPACE-complete). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19060 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the complexity of computing Strahler numbers Ganardi, Moses Lohrey, Markus Computational Complexity Formal Languages and Automata Theory 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. The problem, whether a given context-free grammar in Chomsky normal form produces a derivation tree (resp., an acyclic derivation tree), whose Strahler number is at least a given number $k$ is shown to be P-complete (resp., PSPACE-complete). |
| title | On the complexity of computing Strahler numbers |
| topic | Computational Complexity Formal Languages and Automata Theory |
| url | https://arxiv.org/abs/2512.19060 |