Emergence of order in random languages
Abstract
We consider languages generated by weighted contextfree grammars. It is shown that the behaviour of large texts is controlled by saddlepoint 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 replicasymmetric ansatz, which is valid in the hightemperature, disordered phase. It is shown that in the phase in which languages carry information, the replica symmetry must be broken.
 Publication:

arXiv eprints
 Pub Date:
 February 2019
 arXiv:
 arXiv:1902.07516
 Bibcode:
 2019arXiv190207516D
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Computer Science  Computation and Language;
 Computer Science  Formal Languages and Automata Theory
 EPrint:
 16 pages + 1 appendix