Abstract
Several measures of syntactic complexity in mathematical linguistics allow infinitely many sentences to share a complexity value. Thus there is doubt about the existence of bounds on the memory requirements of parsing mechanisms in terms of the complexities of their inputs. This paper establishes the existence of such bounds for all measures which satisfy certain postulates. The general theorems are applied to the familiar measures of depth, nesting, and self-embedding, as well as to a new measure. The methods of proof lead to unexpected linguistic interpretations of the results.
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