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- W1549978238 abstract "We present effective criteria for first-order definability of regular tree languages. It is known that over words the absence of modulo counting (the “noncounting property”) characterizes the expressive power of first-order logic (McNaughton, Schützenberger), whereas non-counting regular tree languages exist which are not first-order definable. We present new conditions on regular tree languages (more precisely, on tree automata) which imply nondefinability in first-order logic. One method is based on tree homomorphisms which allow to deduce nondefinability of one tree language from nondefinability of another tree language. Additionly we introduce a structural property of tree automata (the socalled Λ-∨-patterns) which also causes tree languages to be undefinable in first-order logic. Finally, it is shown that this notion does not yet give a complete characterization of first-order logic over trees. The proofs rely on the method of Ehrenfeucht-Fraïssé games." @default.
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- W1549978238 date "1995-01-01" @default.
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- W1549978238 title "First-order logic on finite trees" @default.
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- W1549978238 doi "https://doi.org/10.1007/3-540-59293-8_191" @default.
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