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- W2527182206 abstract "The alternation hierarchy in two-variable first-order logic FO2[<] over words was shown to be decidable by Kufleitner and Weil, and independently by Krebs and Straubing. We consider a similar hierarchy, reminiscent of the half levels of the dot-depth hierarchy or the Straubing-Thérien hierarchy. The fragment ${{Sigma }^{2}_{m}}$ of FO2 is defined by disallowing universal quantifiers and having at most m−1 nested negations. The Boolean closure of ${{Sigma }^{2}_{m}}$ yields the m th level of the FO2-alternation hierarchy. We give an effective characterization of ${{Sigma }^{2}_{m}}$ , i.e., for every integer m one can decide whether a given regular language is definable in ${{Sigma }^{2}_{m}}$ . Among other techniques, the proof relies on an extension of block products to ordered monoids." @default.
- W2527182206 created "2016-10-07" @default.
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- W2527182206 date "2016-10-01" @default.
- W2527182206 modified "2023-09-27" @default.
- W2527182206 title "The Half-Levels of the FO2 Alternation Hierarchy" @default.
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- W2527182206 doi "https://doi.org/10.1007/s00224-016-9712-2" @default.
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