Join Our Newsletter

Free Online Productivity Tools
i2Speak
i2Symbol
i2OCR
iTex2Img
iWeb2Print
iWeb2Shot
i2Type
iPdf2Split
iPdf2Merge
i2Bopomofo
i2Arabic
i2Style
i2Image
i2PDF
iLatex2Rtf
Sci2ools

APPROX

2005

Springer

2005

Springer

A string α ∈ Σn is called p-periodic, if for every i, j ∈ {1, . . . , n}, such that i ≡ j mod p, αi = αj, where αi is the i-th place of α. A string α ∈ Σn is said to be period(≤ g), if there exists p ∈ {1, . . . , g} such that α is p-periodic. An property tester for period(≤ g) is a randomized algorithm, that for an input α distinguishes between the case that α is in period(≤ g) and the case that one needs to change at least -fraction of the letters of α, so that it will become period(≤ g). The complexity of the tester is the number of letter-queries it makes to the input. We study here the complexity of testers for period(≤ g) when g varies in the range 1, . . . , n 2 . We show that there exists a surprising exponential phase transition in the query complexity around g = log n. That is, for every δ > 0 and for each g, such that g ≥ (log n)1+δ , the number of queries required and suﬃcient for testing period(≤ g) is polynomial in g. On the othe...

Related Content

Added |
26 Jun 2010 |

Updated |
26 Jun 2010 |

Type |
Conference |

Year |
2005 |

Where |
APPROX |

Authors |
Oded Lachish, Ilan Newman |

Comments (0)