Constraints on Structural Descriptions: Local Transformations

TL;DR: It is shown that the Peters-Ritchie result can be generalized to local transformations and these rules, called "local transformations" not only make precise an informal and briefly discussed notion of Chomsky, but also, generalize it in an appropriate manner.

Abstract: It is very often more convenient and more meaningful to specify a set of structural descriptions analytically rather than generatively, i.e., by specifying a set of constraints each structured description in the set has to satisfy. Peters and Ritchie [7] have shown that if context-sensitive rules are used only for “analysis” then the string language of the set of trees is still context-free. In this paper, we have generalized this result by considering context-free rules constrained by Boolean combinations of proper analysis predicates and domination predicates. These rules, called "local transformations" not only make precise an informal and briefly discussed notion of Chomsky [2], but also, generalize it in an appropriate manner. It is shown that the Peters-Ritchie result can be generalized to local transformations. Linguistic relevance of this result has been also briefly discussed. Results in this paper are relevant to the following situation: Patterns of a class, say A, may be difficult to characteri...