A crevice on the Crane Beach: Finite-degree predicates

  title={A crevice on the Crane Beach: Finite-degree predicates},
  author={Micha{\"e}l Cadilhac and Charles Paperman},
  journal={2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
  • M. Cadilhac, Charles Paperman
  • Published 10 January 2017
  • Computer Science
  • 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
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<inf>0</inf>, and the finite-degree predicates: FO[A<inf>RB</inf>] = FO[≤, MSB<inf>0</inf>, F<inf>IN</inf>]. 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[A<inf>RB</inf>] does not have the… 

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