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Recursive numeral systems are highly regular and easy to process

Paper · 2026 · Ponrawee Prasertsom, Andrea Silvi, Jennifer Culbertson et al.

Summary

Studies of linguistic efficiency usually treat word forms as unanalysable labels and ignore how systematically they are built. Numeral systems expose this gap. Denić and Szymanik (D&S) proposed that recursive counting systems balance lexicon size against average morphosyntactic complexity, but many systems that are optimal under that trade-off are clearly unnatural, for example ones that switch bases from one number to the next. Yang and Regier (Y&R) excluded such systems only by adding hand-crafted grammar constraints.

The authors replace this with a Minimum Description Length framing built on two measures, both computed over numerals for 1–99:

  • Irregularity is the encoding size in bits of the minimal partial DFA that generates exactly a system's numerals.
  • Processing complexity is the cost of encoding the numerals themselves using that automaton.

They compare attested languages from D&S's WALS-based sample with a large set of artificially generated systems, including the previous "optimal" ones. Natural systems turn out to be markedly more regular and easier to process, and this holds under different assumptions about how often numbers are used. The constraints Y&R had to stipulate emerge naturally from regularity, which suggests that efficiency research should account for systematicity across sets of forms.

Key points

  • Possible systems are generated from Hurford's grammar, written as (D, M) pairs of digits and multipliers, over the range 1–99. The DFA is inferred with Mihov and Schulz's algorithm, implemented in the Python package automata-lib.
  • Irregularity in bits follows an adapted Brighton (2003) scheme. It counts the bits needed for the transition table, the initial state and the accepting states. As an example, Karo Batak needs only two rules for 1–99, while English needs extra rules for suppletive forms such as 11 and 12.
  • The space of candidate systems examined exceeds the spaces used by D&S and Y&R put together. Even so, limited compute capped the search depth.
  • The authors acknowledge three limitations: D&S's annotation uses a fixed order, which may inflate measured regularity; the WALS sample over-represents large families such as Indo-European and Austronesian; and it remains untested whether natural systems sit on the Pareto frontier of the new trade-off.
  • Code and data are available at github.com/ponrawee/regularity-processing-complexity-recursive-numerals.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓University of EdinburghEdinburgh · United Kingdom359 works · 77,352 citations🎓University of GothenburgGothenburg · Sweden34 works · 1,625 citations🎓Chalmers University of TechnologyGothenburg · Sweden12 works · 515 citations

 Fields, topics and concepts

📚 Shelves 5The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 worksComputational Theory and Mathematics · 252 works

Cite

Cite as Ponrawee Prasertsom, Andrea Silvi, Jennifer Culbertson, Devdatt Dubhashi, Moa Johansson and Kenny Smith. 2026. Recursive numeral systems are highly regular and easy to process. Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.eacl-long.226

@inproceedings{prasertsom2026recursive,
  title = {{Recursive numeral systems are highly regular and easy to process}},
  author = {Ponrawee Prasertsom, Andrea Silvi, Jennifer Culbertson, Devdatt Dubhashi, Moa Johansson and Kenny Smith},
  booktitle = {Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.eacl-long.226},
  url = {https://doi.org/10.18653/v1/2026.eacl-long.226}
}

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