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A Proof that Every Grammar for English has Self-Embedding to an Unbounded Depth
Authors: Daniel Pohl, Iakovos Koukas, Noam Chomsky Introduction The distinction between competence and performance has played a foundational role in the philosophy of linguistics. Competence is a grasp of the structural properties of all the sentences of a language. Performance involves actual real-time use and may diverge from the underlying competence. Idealizing away from psycholinguistically relevant factors like limits on memory and processing plays a significant role in various essential debates within the field of linguistics. Perhaps the most central and famous is the issue of whether English is a finite-state language. This article provides a proof of the relevant theorem, originally from Chomsky 1959. The claim that any finite-state automaton does not accept English is supported by showing that every grammar for English has self-embedding to an unbounded depth. Self-Embedding The economical production forms for context-free languages, especially the Chomsky normal-for
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