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

  • Authors:
  • Hana Chockler;Orna Kupferman

  • Affiliations:
  • -;-

  • Venue:
  • RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
  • Year:
  • 2002

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Abstract

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