# Strahler Number of Natural Language Sentences in Comparison with Random Trees

arXiv: https://arxiv.org/abs/2307.02697 · HTML: https://mlsanity.com/paper/2307.02697/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 70 references that are in the map.
- First posted on arXiv 6 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [Universal Dependencies v2: An Evergrowing Multilingual Treebank Collection](https://mlsanity.com/paper/2004.10643/) (2020)
- [Criticality in Formal Languages and Statistical Physics](https://mlsanity.com/paper/1606.06737/) (2016)
- [Strongly Incremental Constituency Parsing with Graph Neural Networks](https://mlsanity.com/paper/2010.14568/) (2020)
- [Evaluating Computational Language Models with Scaling Properties of Natural Language](https://mlsanity.com/paper/1906.09379/) (2019)
- [Universal Semantic Parsing](https://mlsanity.com/paper/1702.03196/) (2017)
- [Faster Shift-Reduce Constituent Parsing with a Non-Binary, Bottom-Up Strategy](https://mlsanity.com/paper/1804.07961/) (2018)
- [A Survey of Syntactic-Semantic Parsing Based on Constituent and Dependency Structures](https://mlsanity.com/paper/2006.11056/) (2020)
- [Parsing as Reduction](https://mlsanity.com/paper/1503.00030/) (2015)
- [Taylor's law for Human Linguistic Sequences](https://mlsanity.com/paper/1804.07893/) (2018)
- [Emergence of order in random languages](https://mlsanity.com/paper/1902.07516/) (2019)
- [Discontinuous Grammar as a Foreign Language](https://mlsanity.com/paper/2110.10431/) (2021)
- [Sentence-Incremental Neural Coreference Resolution](https://mlsanity.com/paper/2305.16947/) (2023)
- [Random Language Model](https://mlsanity.com/paper/1809.01201/) (2018)

## Abstract (arXiv)

The Strahler number was originally proposed to characterize the complexity of river bifurcation and has found various applications. This article proposes computation of the Strahler number's upper and lower limits for natural language sentence tree structures. Through empirical measurements across grammatically annotated data, the Strahler number of natural language sentences is shown to be almost 3 or 4, similarly to the case of river bifurcation as reported by Strahler (1957). From the theory behind the number, we show that it is one kind of lower limit on the amount of memory required to process sentences. We consider the Strahler number to provide reasoning that explains reports showing that the number of required memory areas to process sentences is 3 to 4 for parsing (Schuler et al., 2010), and reports indicating a psychological "magical number" of 3 to 5 (Cowan, 2001). An analytical and empirical analysis shows that the Strahler number is not constant but grows logarithmically; therefore, the Strahler number of sentences derives from the range of sentence lengths. Furthermore, the Strahler number is not different for random trees, which could suggest that its origin is not specific to natural language.