Indistinguishability and First-Order Logic

  • Skip Jordan
  • Thomas Zeugmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4978)


The “richness” of properties that are indistinguishable from first-order properties is investigated. Indistinguishability is a concept of equivalence among properties of combinatorial structures that is appropriate in the context of testability. All formulas in a restricted class of second-order logic are shown to be indistinguishable from first-order formulas. Arbitrarily hard properties, including RE-complete properties, that are indistinguishable from first-order formulas are shown to exist. Implications on the search for a logical characterization of the testable properties are discussed.


Property testing logic graph theory descriptive complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Skip Jordan
    • 1
  • Thomas Zeugmann
    • 1
  1. 1.Division of Computer ScienceHokkaido UniversitySapporoJapan

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