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Regular languages and associative language descriptions

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.
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Marcella Anselmo, Alessandra Cherubini, Pierluigi San Pietro. Regular languages and associative language descriptions. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2007, 9 (2), pp.153--173. ⟨hal-00966526⟩

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