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Asveld, P.R.J. (1977) Extensions of Language Families and Canonical Forms for Full AFL-Structures. Memorandum 167, Department of Applied Mathematics, University of Twente, Enschede. ISSN 0169-2690
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We consider the following ways of extending a family of languages to an "enriched" family : (i) hyper-algebraic extension () based on iterated parallel substitution, (ii) algebraic extension () obtained by nested iterated substitution, (iii) rational extension () achieved by not-self-embedding nested iterated substitution, and (iv) a few subrational extensions () based on several kinds of substitution. We introduce full -AFL's, i.e. nontrivial families closed under finite substitution, intersection with regular sets and under , which turn out to be equivalent to well-known AFL-structures such as full hyper-AFL (), super-AFL (), substitution-closed AFL (), semi-AFL (), etc. Then we establish Canonical Forms for the smallest full -AFL containing , i.e. we decompose the operator into simpler operators. Using Canonical Forms for full -AFL's we obtain expressions for the smallest full -AFL containing the result of substituting a family of languages into another family.
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