Emergence of order in random languages

@article{DeGiuli2019EmergenceOO,
  title={Emergence of order in random languages},
  author={E. DeGiuli},
  journal={ArXiv},
  year={2019},
  volume={abs/1902.07516}
}
  • E. DeGiuli
  • Published 2019
  • Computer Science, Physics, Mathematics
  • ArXiv
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… Expand
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References

SHOWING 1-10 OF 27 REFERENCES
Random Language Model.
  • E. DeGiuli
  • Computer Science, Medicine
  • Physical review letters
  • 2019
TLDR
A model of random languages, defined by weighted context-free grammars, is considered, finding a transition is found from a random phase, in which sentences are indistinguishable from noise, to an organized phase in which nontrivial information is carried. Expand
Criticality in Formal Languages and Statistical Physics
We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a powerExpand
Critical Behavior in Physics and Probabilistic Formal Languages
TLDR
It is proved that Markov/hidden Markov processes generically exhibit exponential decay in their mutual information, which explains why natural languages are poorly approximated by Markov process, and presents a broad class of models that naturally reproduce this critical behavior. Expand
The ising model on a random planar lattice: The structure of the phase transition and the exact critical exponents
Abstract We investigate the critical properties of a recently proposed exactly soluble Ising model on a planar random dynamical lattice representing a regularization of the zero-dimensional stringExpand
Introduction to Automata Theory, Languages and Computation
TLDR
This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments. Expand
Statistical physics of language dynamics
Language dynamics is a rapidly growing field that focuses on all processes related to the emergence, evolution, change and extinction of languages. Recently, the study of self-organization andExpand
Ising model on a dynamical planar random lattice: Exact solution
Abstract The Ising model on a collection of all planar lattices with coordination number 4 is shown to be equivalent to the exactly solvable two-matrix model in the large N limit. The sum over allExpand
Spin glasses on Bethe lattices for large coordination number
Abstract:We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate theExpand
Spin Glasses on Thin Graphs
Abstract In a recent paper [C. Baillie, D.A. Johnston and J.-P. Kownacki, Nucl. Phys. B 432 (1994) 551] we found strong evidence from simulations that the Ising antiferromagnet on “thin” randomExpand
Analytic Combinatorics
TLDR
This text can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study, and is certain to become the definitive reference on the topic. Expand
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