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

P.R.J. Asveld

    Research output: Book/ReportReportOther research output

    Abstract

    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

    Keywords

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

    Cite this

    Asveld, P. R. J. (1976). Extensions of Families of Languages: Lattices of Full X-AFL's. Enschede: University of Twente, Department of Applied Mathematics.
    Asveld, P.R.J. / Extensions of Families of Languages: Lattices of Full X-AFL's. Enschede : University of Twente, Department of Applied Mathematics, 1976. 34 p.
    @book{1c3e7a84d320434da37e73e2d511c45c,
    title = "Extensions of Families of Languages: Lattices of Full X-AFL's",
    abstract = "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.",
    keywords = "EWI-3696, HMI-SLT: Speech and Language Technology",
    author = "P.R.J. Asveld",
    note = "Research supported by Netherlands Organization for the Advancement of Pure Research (ZWO).",
    year = "1976",
    language = "Undefined",
    publisher = "University of Twente, Department of Applied Mathematics",

    }

    Asveld, PRJ 1976, Extensions of Families of Languages: Lattices of Full X-AFL's. University of Twente, Department of Applied Mathematics, Enschede.

    Extensions of Families of Languages: Lattices of Full X-AFL's. / Asveld, P.R.J.

    Enschede : University of Twente, Department of Applied Mathematics, 1976. 34 p.

    Research output: Book/ReportReportOther research output

    TY - BOOK

    T1 - Extensions of Families of Languages: Lattices of Full X-AFL's

    AU - Asveld, P.R.J.

    N1 - Research supported by Netherlands Organization for the Advancement of Pure Research (ZWO).

    PY - 1976

    Y1 - 1976

    N2 - 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.

    AB - 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.

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    KW - HMI-SLT: Speech and Language Technology

    M3 - Report

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

    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

    ER -

    Asveld PRJ. Extensions of Families of Languages: Lattices of Full X-AFL's. Enschede: University of Twente, Department of Applied Mathematics, 1976. 34 p.