Abstract
Chomsky (1959a) presented an algorithm for constructing a finite transducer that is strongly equivalent to a Chomsky-normal-form context-free grammar for all sentences generated by that grammar with up to any specified finite degree of center embedding. This article presents a new solution using a variety of COORDINATE GRAMMAR to assign nonembedding (paratactic) structures strongly equivalent to those assigned by an embedding grammar, which can in turn be directly computed by a finite transducer. It proposes that the bound on center embedding is really a consequence of a bound on alternation between right and left embedding, called here ZIGZAG EMBEDDING . Coordinate grammars can also be used to assign nonembedding structures equivalent to those with up to any specified finite degree of coordinate embedding (the occurrence of a coordinate structure as a member of a coordinate structure of the same type). It concludes that coordinate grammars or the finite transducers strongly equivalent to them are psychologically real, and that the existence of a finite bound on the degree of zigzag and coordinate embedding is a consequence of the increasing size and complexity of such grammars or transducers as the bound increases.
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