### 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 |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 7 |

Publication status | 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.