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

We continue the study of combinatorial property testing. For a property ψ, an ψ-test for ψ, for 0< ≤ 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 ψ-far from satisfying ψ, where ψ-far essentially means that an ψ-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 -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) toω-regular languages: given a nondeterministic Büchi automaton script A sign 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 · y^ω, for finite words x and y, samples only a constant number of letters in x and y, returns"yes" if ω ε L(script A sign), and returns"no" with probability 2/3 if ω is ε-far from L(script A sign). We also discuss the applicability of property testing to formal verification, whereω-regular languages are used for the specification of the behavior of nonterminating reactive systems, and computations correspond to lasso-shape words.