Four Hierarchies of ω-Regular Languages

概要

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We argue several decompositions of ω-regular sets into rational G_δ sets. We measure the complexity of ω-regular sets by the number of rational G_δ sets obtained by the decompositions. Barua (1992) studied a hierarchy R_n(n=1, 2, 3,…), where R_n is a class of ω-regular sets which are decomposed into n rational G_δ sets forming a decreasing sequence. On the other hand, Kaminski (1985) defined a hierarchy B_m(m=1, 2, 3,…), where B_m is a class of ω-regular sets which are decomposed into 2m rational G_δ sets not necessarily forming a decreasing sequence. Already it is reported that B_n=R_<2n> by Takahashi (1995). And besides we show B_n=R_<2n>, where B_n is a class of ω-regular sets whose defining condition is more lenient than that of R_<2n>. In conclusion, we state that various hierarchies are reduced to four types of hierarchies.
横浜商科大学の論文
1998-03-01