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

P.R.J. Asveld

Research output: Book/ReportReportOther research output

### 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 language Undefined Enschede University of Twente, Department of Applied Mathematics 7 Published - 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.
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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.
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.