English

Emergence of order in random languages

Disordered Systems and Neural Networks 2022-10-03 v3 Computation and Language Formal Languages and Automata Theory

Abstract

We consider languages generated by weighted context-free grammars. It is shown that the behaviour of large texts is controlled by saddle-point equations for an appropriate generating function. We then consider ensembles of grammars, in particular the Random Language Model of E. DeGiuli, Phys. Rev. Lett., 122, 128301, 2019. This model is solved in the replica-symmetric ansatz, which is valid in the high-temperature, disordered phase. It is shown that in the phase in which languages carry information, the replica symmetry must be broken.

Keywords

Cite

@article{arxiv.1902.07516,
  title  = {Emergence of order in random languages},
  author = {Eric De Giuli},
  journal= {arXiv preprint arXiv:1902.07516},
  year   = {2022}
}

Comments

16 pages + 2 appendices; v2: references added and some explanations expanded. v3: Corrigendum added as Appendix B

R2 v1 2026-06-23T07:45:55.433Z