ω-Regular languages are testable with a constant number of queries

  • Authors:

  • Hana Chockler;Orna Kupferman

  • Affiliations:

  • College of Computer and Information Science, Northeastern University, Boston, MA and Hebrew University of Jerusalem, Israel;School of Engineering and Computer Science, Hebrew University, Jerusalem 91904, Israel

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2004

Quantified Score

Hi-index 5.23

Visualization

Abstract

We continue the study of combinatorial property testing. For a property ψ, an ε-test for ψ, for 0 x, returns "yes" if x satisfies ψ, and returns "no" with high probability if x is ε-far from satisfying ψ, where ε-far essentially means that an ε-fraction of x needs to be changed in order for it to satisfy ψ. In (Proceedings of the 40th IEEE Symposium on Foundations of Computer Science, 1999, pp. 645-655), Alon et al. show that regular languages are ε-testable with a constant (depends on ψ and ε and independent of x) number of queries. We extend the result in (Proceedings of the 40th IEEE Symposium on Foundations of Computer Science, 1999, pp. 645-655) to ω-regular languages: given a nondeterministic Büchi automaton A on infinite words and a small ε 0, we describe an algorithm that gets as input an infinite lasso-shape word of the form x ċ yω, 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 ε-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.