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

Peter R. J. Asveld ()
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Peter R. J. Asveld: Twente University of Technology, Department of Computer Science

Chapter Chapter 15 in Where Mathematics, Computer Science, Linguistics and Biology Meet, 2001, pp 175-186 from Springer

Abstract: Abstract We investigate different sets of operations on languages which result 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 C m (m ⩾ 1) of classes of such algebraic structures (full AFL-structures): each class is a proper superset of the next class (C m ⊃ C m +1). In turn each class C m contains a countably infinite hierarchy, i.e. a countably infinite chain of language families K m,n (n ⩾ 1) such that (i) each K m,n is closed under the operations that determine C m and (ii) each K m,n is properly included in the next one: K m,n ⊂ K m,n+1.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9634-3_15

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DOI: 10.1007/978-94-015-9634-3_15

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