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An Infinite Sequence of Full AFL-Structures, Each of Which Possesses an Infinite Hierarchy

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Asveld, Peter R.J. (1999) An Infinite Sequence of Full AFL-Structures, Each of Which Possesses an Infinite Hierarchy. [Report]

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Abstract:We investigate different sets of operations on languages which results in corresponding algebraic structures, viz.\ in different types of full AFL's (full Abstract Family of Languages). By iterating control on ETOL-systems we show that there exists an infinite sequence ${\cal C}_m$ ($m\geq1$) of classes of such algebraic structures (full AFL-structures): each class is a proper superset of the next class $({\cal C}_m\supset{\cal C}_{m+1})$. In turn each class ${\cal C}_m$ contains a countably infinite hierarchy, i.e., a countably infinite chain of language families $K_{m,n}$ ($n\geq1$) such that (i) each $K_{m,n}$ is closed under the operations that determine ${\cal C}_m$, and (ii) each $K_{m,n}$ is properly included in the next one: $K_{m,n}\subset K_{m,n+1}$.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/64304
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