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Rectangular Algebras as Tree Recognizers
Tekijät: Steinby Magnus
Kustantaja: UNIV SZEGED, FAC SCIENCE
Julkaisuvuosi: 2015
Lehti:Acta Cybernetica
Tietokannassa oleva lehden nimiACTA CYBERNETICA
Lehden akronyymi: ACTA CYBERN
Vuosikerta: 22
Numero: 2
Aloitussivu: 499
Lopetussivu: 515
Sivujen määrä: 17
ISSN: 0324-721X
DOI: https://doi.org/10.14232/actacyb.22.2.2015.15
Tiivistelmä
We consider finite rectangular algebras of finite type as tree recognizers. The type is represented by a ranked alphabet Sigma. We determine the varieties of finite rectangular Sigma-algebras and show that they form a Boolean lattice in which the atoms are minimal varieties of finite Sigma-algebras consisting of projection algebras. We also describe the corresponding varieties of E-tree languages and compare them with some other varieties studied in the literature. Moreover, we establish the solidity properties of these varieties of finite algebras and tree languages. Rectangular algebras have been previously studied by R. Poschel and M. Reichel (1993), and we make use of some of their results.
We consider finite rectangular algebras of finite type as tree recognizers. The type is represented by a ranked alphabet Sigma. We determine the varieties of finite rectangular Sigma-algebras and show that they form a Boolean lattice in which the atoms are minimal varieties of finite Sigma-algebras consisting of projection algebras. We also describe the corresponding varieties of E-tree languages and compare them with some other varieties studied in the literature. Moreover, we establish the solidity properties of these varieties of finite algebras and tree languages. Rectangular algebras have been previously studied by R. Poschel and M. Reichel (1993), and we make use of some of their results.
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