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- W2956143764 abstract "First-order logic (FO) over words is shown to be equiexpressive with FO equipped with a restricted set of numerical predicates, namely the order, a binary predicate MSB$_0$, and the finite-degree predicates: FO[Arb] = FO[<, MSB$_0$, Fin]. The Crane Beach Property (CBP), introduced more than a decade ago, is true of a logic if all the expressible languages admitting a neutral letter are regular. Although it is known that FO[Arb] does not have the CBP, it is shown here that the (strong form of the) CBP holds for both FO[<, Fin] and FO[<, MSB$_0$]. Thus FO[<, Fin] exhibits a form of locality and the CBP, and can still express a wide variety of languages, while being one simple predicate away from the expressive power of FO[Arb]. The counting ability of FO[<, Fin] is studied as an application." @default.
- W2956143764 created "2019-07-12" @default.
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- W2956143764 date "2017-06-01" @default.
- W2956143764 modified "2023-09-25" @default.
- W2956143764 title "A crevice on the Crane Beach: Finite-degree predicates" @default.
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- W2956143764 doi "https://doi.org/10.1109/lics.2017.8005148" @default.
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