Three Notes on Controlled Hyper-Algebraic and Dhyper-Algebraic Extensions

P.R.J. Asveld

    Research output: Book/ReportReportOther research output

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    Abstract

    (1) Regular control does not increase the generating power of 1-restricted [d]$K$-iteration grammars provided that $K\supseteq{\rm SYMBOL}$, and $K$ is closed under isomorphism and under union with ${\rm SYMBOL}$-languages. (2) Let $\Gamma$ be a prequasoid closed under the regular operations. If $K$ is a prequasoid [pseudoid], then $H(\Gamma)\subseteq H(\Gamma,K)$ [$\eta(\Gamma) \subseteq\eta(\Gamma,K)$. In particular we have $H(\Gamma) \subseteq (\Gamma){\rm ETOL}$ and $\eta(\Gamma) \subseteq (\Gamma){\rm EDTOL}$.(3) Underweak assumptions on $\Gamma$ and $K$, the decidability of the emptiness problem for $\Gamma$ and $K$ implies the decidability of the emptiness problem and the membership problem for the families $\eta(\Gamma,K)$ and $\eta(K)$.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages7
    Publication statusPublished - 1977

    Keywords

    • HMI-SLT: Speech and Language Technology
    • EWI-3714

    Cite this

    Asveld, P. R. J. (1977). Three Notes on Controlled Hyper-Algebraic and Dhyper-Algebraic Extensions. Enschede: University of Twente, Department of Applied Mathematics.
    Asveld, P.R.J. / Three Notes on Controlled Hyper-Algebraic and Dhyper-Algebraic Extensions. Enschede : University of Twente, Department of Applied Mathematics, 1977. 7 p.
    @book{a481e990d6f940e78e47a1d72712815d,
    title = "Three Notes on Controlled Hyper-Algebraic and Dhyper-Algebraic Extensions",
    abstract = "(1) Regular control does not increase the generating power of 1-restricted [d]$K$-iteration grammars provided that $K\supseteq{\rm SYMBOL}$, and $K$ is closed under isomorphism and under union with ${\rm SYMBOL}$-languages. (2) Let $\Gamma$ be a prequasoid closed under the regular operations. If $K$ is a prequasoid [pseudoid], then $H(\Gamma)\subseteq H(\Gamma,K)$ [$\eta(\Gamma) \subseteq\eta(\Gamma,K)$. In particular we have $H(\Gamma) \subseteq (\Gamma){\rm ETOL}$ and $\eta(\Gamma) \subseteq (\Gamma){\rm EDTOL}$.(3) Underweak assumptions on $\Gamma$ and $K$, the decidability of the emptiness problem for $\Gamma$ and $K$ implies the decidability of the emptiness problem and the membership problem for the families $\eta(\Gamma,K)$ and $\eta(K)$.",
    keywords = "HMI-SLT: Speech and Language Technology, EWI-3714",
    author = "P.R.J. Asveld",
    note = "Research supported by Netherlands Organization for the Advancement of Pure Research (ZWO).",
    year = "1977",
    language = "Undefined",
    publisher = "University of Twente, Department of Applied Mathematics",

    }

    Asveld, PRJ 1977, Three Notes on Controlled Hyper-Algebraic and Dhyper-Algebraic Extensions. University of Twente, Department of Applied Mathematics, Enschede.

    Three Notes on Controlled Hyper-Algebraic and Dhyper-Algebraic Extensions. / Asveld, P.R.J.

    Enschede : University of Twente, Department of Applied Mathematics, 1977. 7 p.

    Research output: Book/ReportReportOther research output

    TY - BOOK

    T1 - Three Notes on Controlled Hyper-Algebraic and Dhyper-Algebraic Extensions

    AU - Asveld, P.R.J.

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

    PY - 1977

    Y1 - 1977

    N2 - (1) Regular control does not increase the generating power of 1-restricted [d]$K$-iteration grammars provided that $K\supseteq{\rm SYMBOL}$, and $K$ is closed under isomorphism and under union with ${\rm SYMBOL}$-languages. (2) Let $\Gamma$ be a prequasoid closed under the regular operations. If $K$ is a prequasoid [pseudoid], then $H(\Gamma)\subseteq H(\Gamma,K)$ [$\eta(\Gamma) \subseteq\eta(\Gamma,K)$. In particular we have $H(\Gamma) \subseteq (\Gamma){\rm ETOL}$ and $\eta(\Gamma) \subseteq (\Gamma){\rm EDTOL}$.(3) Underweak assumptions on $\Gamma$ and $K$, the decidability of the emptiness problem for $\Gamma$ and $K$ implies the decidability of the emptiness problem and the membership problem for the families $\eta(\Gamma,K)$ and $\eta(K)$.

    AB - (1) Regular control does not increase the generating power of 1-restricted [d]$K$-iteration grammars provided that $K\supseteq{\rm SYMBOL}$, and $K$ is closed under isomorphism and under union with ${\rm SYMBOL}$-languages. (2) Let $\Gamma$ be a prequasoid closed under the regular operations. If $K$ is a prequasoid [pseudoid], then $H(\Gamma)\subseteq H(\Gamma,K)$ [$\eta(\Gamma) \subseteq\eta(\Gamma,K)$. In particular we have $H(\Gamma) \subseteq (\Gamma){\rm ETOL}$ and $\eta(\Gamma) \subseteq (\Gamma){\rm EDTOL}$.(3) Underweak assumptions on $\Gamma$ and $K$, the decidability of the emptiness problem for $\Gamma$ and $K$ implies the decidability of the emptiness problem and the membership problem for the families $\eta(\Gamma,K)$ and $\eta(K)$.

    KW - HMI-SLT: Speech and Language Technology

    KW - EWI-3714

    M3 - Report

    BT - Three Notes on Controlled Hyper-Algebraic and Dhyper-Algebraic Extensions

    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

    ER -

    Asveld PRJ. Three Notes on Controlled Hyper-Algebraic and Dhyper-Algebraic Extensions. Enschede: University of Twente, Department of Applied Mathematics, 1977. 7 p.