Abstract
The Associative Language Description model (ALD) is a combination of locally testable and constituent structure ideas. It is consistent with current views on brain organization and can rather conveniently describe typical technical languages such as Pascal or HTML. ALD languages are strictly enclosed in context-free languages but in practice the ALD model equals CF grammars in explanatory adequacy. Various properties of ALD have been investigated, but many theoretical questions are still open. For instance, it is unknown, at the present, whether the ALD family includes the regular languages. Here it is proved that several known classes of regular languages are ALD: threshold locally testable languages, group languages, positive commutative languages and commutative languages on 2-letter alphabets. Moreover, we show that there is an ALD language in each level of (restricted) star height hierarchy. These results seem to show that ALD languages are well-distributed over the class of regular languages.
Highlights
The Associative Language Description model (ALD) (6) was originally motivated by the want of a brain compatible theory of language
We show that regular threshold locally testable languages (3), regular positive commutative languages, regular commutative languages on an alphabet of at most two elements and regular group languages are all ALD languages
We show how to solve the problem in two particular cases: regular languages in Com+ (Proposition 3.21); and regular commutative languages on alphabets with two letters at most (Proposition 3.22)
Summary
The Associative Language Description model (ALD) (6) was originally motivated by the want of a brain compatible theory of language. In essence, this definition combines the concepts of local testability and of phrase structure in as simple a way as possible, aligned with current views on. Many basic properties of the ALD model were established in (1) and in (2), such as: nonclosure under union, concatenation and homomorphism; strict inclusion in the CF family (only noncounting context-free languages are ALD); comparison with other families; hierarchy theorems; etc. There is an ALD language in each level of the (restricted) star hierarchy All these results seem to show that ALD languages are “well-distributed” over the class of regular languages.
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