Abstract
| Original language | Undefined |
|---|---|
| Place of Publication | Enschede |
| Publisher | University of Twente, Department of Applied Mathematics |
| Number of pages | 34 |
| Publication status | Published - 1976 |
Keywords
- EWI-3696
- HMI-SLT: Speech and Language Technology
Cite this
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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/Report › Report › Other 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.
KW - EWI-3696
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 -