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- W1567392832 abstract "Let TL[X;F] (TL[F]) be the class of formulas of temporal logic, where as the only temporal operatorsX (next) and F (eventually) are allowed (only F is allowed, resp.). For a class TL[X;F] let L( ) be the class of -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]) = Sk 0 L(TL[X(k);F]) and L(TL[F]) = L(TL[X(0);F]). We prove a levelwise characterization of the above syntactical hierarchy (1) in terms of a certain pattern Srev k (cf. Figure 6) that must not appear in the transition graph of deterministic finite automata, and (2) in terms of a formal language representation involving k-leftdeterministic languages. With (1) we generalize the known forbidden pattern for L(TL[F]) which is Srev 0 and in (2) we carry over the notion of leftdeterministic languages to decompositions of words into consecutive blocks of length k + 1. Our characterization enables us to give concise proofs of strictness and decidability results for the family of classes L(TL[X(k);F]) k 0 . As a by-product, we reproof the known forbidden pattern characterization for L(TL[X;F]) in a novel way and we learn, how the pattern Srev 0 turns into the pattern for L(TL[X;F]) as level k increases. All results hold dually for restricted past temporal logic, k-rightdeterministic languages and the pattern Sk (cf. Figure 5). We point out similarities and differences to languages having dot-depth one." @default.
- W1567392832 created "2016-06-24" @default.
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- W1567392832 date "2007-01-01" @default.
- W1567392832 modified "2023-09-27" @default.
- W1567392832 title "Generalized Deterministic Languages and their Automata: A Characterization of Restricted Temporal Logic" @default.
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