Extensions of Families of Languages: Lattices of Full X-AFL's

P.R.J. Asveld

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    This paper is a continuation of our research on $X$-extensions and full $X$-AFL's. We discuss the algebraic structure of the class of all full $X$-AFL's and establish a Canonical Form Theorem for full $X$-AFL's (similar to a theorem for full AFL's obtained earlier by Ginsburg & Spanier (1971)) i.e. we prove $\hat{\cal X}(K) = X\Pi(K)$, where $K$ is an arbitrary family, $\hat{\cal X}(K)$ [$\Pi(K)$] is the least full $X$-AFL [pre-quasoid] containing $K$, and $X$ is the $X$-extension. We consider full ($X$-)principal $X$-AFL's and full sub-$X$-AFL's of a given full $X$-AFL from the point of view of universal algebra and lattice theory. In order to fit some well-known results on full (semi-)AFL's in our framework of extensions, we introduce a few subrational extensions and establish the corresponding Canonical Form Theorems for full (semi-)AFL's. For a restricted class of language families we show another Canonical Form Theorem and finally we discuss some semigroups consisting of operators on families of languages.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages34
    Publication statusPublished - 1976


    • EWI-3696
    • HMI-SLT: Speech and Language Technology

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