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.

翻译：我们考虑由加权的无上下文语法产生的语言,显示大文本的行为由用于适当生成功能的马鞍点方程式控制。然后我们考虑语法组合,特别是E.DeGiuli、Phys.Rev.Lett的随机语言模型,122、128301、2019。这个模型在对称的反射中解决,在高温、无序阶段有效。它表明,在语言传递信息的阶段,复制的对称必须打破。