Associative language descriptions

AbstractThe new Associative Language Description (ALD) model, a combination of locally testable and constituent structure ideas, is proposed, arguing that in practice it equals context-free (CF) grammars in explanatory adequacy, yet it provides a simple description and it excludes mathematical sets based on counting properties, which are rarely (if ever) used in compiler construction or in computational linguistics. The ALD model has been recently proposed as an approach consistent with current views on brain organization. ALD is a “pure”, i.e., nonterminal-free definition. The strict inclusion of ALD languages in CF languages is proved, based on a lemma which strengthens the Pumping Lemma for CF languages. Basic nonclosure and undecidability properties are considered and compared with those of CF languages. It is shown that the hardest context-free language is in ALD, that there exists a hierarchy of ALD languages and that each ALD tree language enjoys the noncounting property of parenthesized CF languages. Typical technical languages (Pascal, HTML) can be rather conveniently described by ALD rules