### Abstract

We continue the study of combinatorial property testing, initiated by Goldreich, Goldwasser, and Ron in [J. ACM, 45 (1998), pp. 653-750]. The subject of this paper is testing regular languages. Our main result is as follows. For a regular language L £{0,1} and an integer n there exists a randomized algorithm which always accepts a word w of length n if tu £L and rejects it \vith high probability if w has to be modified in at least en positions to create a word in L. The algorithm queries O(l/e) bits of w. This query complexity is shown to be optimal up to a factor polylogarithmic in 1/e. We also discuss the testability of more complex languages and show, in particular, that the query complexity required for testing context-free languages cannot be bounded by any function of (.. The problem of testing regular languages can be viewed as a part of a very general approach, seeking to probe testability of properties defined by logical means.

Original language | English (US) |
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Pages (from-to) | 1842-1862 |

Number of pages | 21 |

Journal | SIAM Journal on Computing |

Volume | 30 |

Issue number | 6 |

DOIs | |

State | Published - 2000 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Mathematics(all)

### Keywords

- Context-free languages
- Property testing
- Regular languages

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## Cite this

*SIAM Journal on Computing*,

*30*(6), 1842-1862. https://doi.org/10.1137/s0097539700366528