Untestable Properties Expressible with Four First-Order Quantifiers

  • Charles Jordan
  • Thomas Zeugmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6031)

Abstract

In property testing, the goal is to distinguish between structures that have some desired property and those that are far from having the property, after examining only a small, random sample of the structure. We focus on the classification of first-order sentences based on their quantifier prefixes and vocabulary into testable and untestable classes. This classification was initiated by Alon et al. [1], who showed that graph properties expressible with quantifier patterns ∃ * ∀ * are testable but that there is an untestable graph property expressible with quantifier pattern ∀ * ∃ *. In the present paper, their untestable example is simplified. In particular, it is shown that there is an untestable graph property expressible with each of the following quantifier patterns: ∀ ∃ ∀ ∃, ∀ ∃ ∀ 2, ∀ 2 ∃ ∀ and ∀ 3 ∃.

Keywords

property testing logic 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Charles Jordan
    • 1
  • Thomas Zeugmann
    • 1
  1. 1.Division of Computer ScienceHokkaido University, N-14, W-9SapporoJapan

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