ω-Regular Languages Are Testable with a Constant Number of Queries

  • Hana Chockler
  • Orna Kupferman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2483)


We continue the study of combinatorial property testing. For a property ψ, an ɛ-test for ψ, for 0 < ɛ 1, is a randomized algorithm that given an input x, returns “yes” if x satisfies ψ, and returns “no” with high probability if x is ɛ-far from satisfying ψ, where ɛ-far essentially means that an ɛ-fraction of x needs to be changed in order for it to satisfy ψ. In [AKNS99], Alon et al. show that regular languages are ɛ-testable with a constant (depends on ψ and ɛ and independent of x) number of queries. We extend the result in [AKNS99] to ω-regular languages: given a nondeterministic Büchi automaton A on infinite words and a small ɛ > 0, we describe an algorithm that gets as input an infinite lasso-shape word of the form x · y ω, for finite words x and y, samples only a constant number of letters in x and y, returns “yes” if w ∈ L(A), and returns “no” with probability 2/3 if w is ɛ-far from L(A). We also discuss the applicability of property testing to formal verification, where ω-regular languages are used for the specification of the behavior of nonterminating reactive systems, and computations correspond to lasso-shape words.


Model Check Regular Language Query Complexity Property Testing Input Word 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Hana Chockler
    • 1
  • Orna Kupferman
    • 1
  1. 1.School of Engineering and Computer ScienceHebrew UniversityJerusalemIsrael

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