Three Notes on Controlled Hyper-Algebraic and Dhyper-Algebraic Extensions
P.R.J. Asveld · University of Twente Research Information · 1977
(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 $\\eta(K)$.