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A Refutation of Finite-State Language Models through Zipf's Law for Factual Knowledge.

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This study introduces perigraphic processes as a semantic model for natural language, distinct from finite-state models. These processes capture knowledge via Zipf

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Area of Science:

  • Theoretical computer science
  • Computational linguistics
  • Statistical language modeling

Background:

  • Finite-state processes are widely used in statistical language modeling but primarily capture syntactic rather than semantic properties.
  • A novel theoretical framework is proposed to model semantic properties of natural language texts.

Purpose of the Study:

  • To present a hypothetical argument against the sufficiency of finite-state processes for capturing semantic properties in language modeling.
  • To introduce and define perigraphic processes as a theoretical model for semantic properties.
  • To demonstrate the disjointness between finite-state and perigraphic processes.

Main Methods:

  • Defining perigraphic processes based on Zipf-law accumulation of time-independent, compressed, and inferrable factual knowledge.
  • Establishing the disjointness of finite-state and perigraphic processes using the Hilberg condition (power-law growth of algorithmic mutual information).
  • Introducing Oracle processes as a simple example of perigraphic processes and demonstrating their adherence to the Hilberg condition via the data-processing inequality.

Main Results:

  • Finite-state processes and perigraphic processes are mathematically disjoint classes.
  • Finite-state processes do not satisfy the Hilberg condition.
  • Oracle processes, a type of perigraphic process, satisfy the Hilberg condition.

Conclusions:

  • Finite-state processes are insufficient for fully capturing the semantic properties of natural language.
  • Perigraphic processes offer a promising theoretical alternative for semantic modeling in language.
  • The findings have implications for the development of more semantically aware statistical language models.