On Twist-closed Trios
نویسنده
چکیده
The language theoretic operation twist from [JaPe 87] is studied in connection with the semiAFLs of languages accepted by reversal bounded multipushdown and multicounter acceptors. It is proved that the least twist -closed trio generated by MIR := fwwrev j w 2 fa; bg g is equal to the family of languages accepted in quasirealtime by nondeterministic one-way multipushdown acceptors which operate in such a way that in every computation each pushdown makes at most one reversal. Thus, M\(MIR) =Mtwist(MIR) and this family is principal both as a twist -closed and as an intersection -closed semiAFL. This is in contrast to the semiAFL of languages accepted by reversal-bounded multicounter machines in quasi-realtime. This family is a well known semiAFL which is principal as an intersection -closed semiAFL with generator B1 := fan1an1 j n 2 INg, see [Grei 78], but is not principal as a semiAFL. It is here shown that it forms a hierarchy of twist -closed semiAFLs and therefore cannot be principal as twist -closed semiAFL. Zusammenfassung Die in [JaPe 87] de nierte Operation twist auf Wortern und formalen Sprachen wird untersucht in Verbindung mit den semiAFL's der von umkehrbeschr ankten Kellerund Z ahlerautomaten akzeptierten Sprachen. Es wird gezeigt, da das kleinste, von der Sprache MIR := fwwrev j w 2 fa; bg g generierte twist -abgeschlossene Trio identisch ist mit der Familie aller Sprachen, die von mehr-Kellerautomaten in quasi-Realzeit mit umkehrbeschr ankten Kellern akzeptiert werden. Daher ist M\(MIR) = Mtwist(MIR) als durchschnitts und als twist -abgeschlossenes Trio eine sogenannte Haupt-semiAFL (principal semiAFL). Im Unterschied dazu ist die Familie M\(B1), mit Generator B1 := fan1an1 j n 2 INg, der in quasi-Realzeit von umkehrbeschr anktenmehr-Z ahlerautomaten akzeptierten Sprachen, vergl. [Grei 78], zwar twist -abgeschlossen, aber es gilt nicht M\(B1) =Mtwist(B1). 0
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