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by Heinz Schmitz, Theoretische Informatik
Inst. fur Informatik, Univ. Wurzburg
ftp://ftp-info4.informatik.uni-wuerzburg.de/pub/TRs/schmitz99a.ps.gz
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Abstract:
Let TL[X; F] (TL[F]) be the class of formulas of temporal logic, where as the only temporal operators X (next) and F (eventually) are allowed (only F is allowed, resp.). For a class \Phi ` TL[X; F] let L(\Phi) be the class of \Phi-definable languages. Among others, characterizations of L(TL[X; F]) and L(TL[F]) in terms of forbidden patterns in finite automata are known. Here we ask for every bound k 0 on the number of nested uses of the next operator for the expressive power of the respective fragment of TL[X; F]. Denote by TL[X(k); F] the class of formulas in TL[X; F] with nesting depth k in the next operator. Obviously, L(TL[X; F]) =
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