## Abstract

We continue the study of combinatorial property testing. For a property ψ, an ε-test for ψ, for 0 < ε ≤ 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 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 [AKNS99], 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 [AKNS99] to ω-regular languages: given a nondeterministic Büchi automaton A on infinite words and a smallε > 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 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.

Original language | American English |
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Title of host publication | Randomization and Approximation Techniques in Computer Science - 6th International Workshop, RANDOM 2002, Proceedings |

Editors | Salil Vadhan, Jose D. P. Rolim |

Publisher | Springer Verlag |

Pages | 26-38 |

Number of pages | 13 |

ISBN (Print) | 3540441476, 9783540457268 |

DOIs | |

State | Published - 2002 |

Event | 6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002 - Cambridge, United States Duration: 13 Sep 2002 → 15 Sep 2002 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2483 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 6th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2002 |
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Country/Territory | United States |

City | Cambridge |

Period | 13/09/02 → 15/09/02 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2002.