Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Near-optimal sparse fourier representations via sampling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Property testing of data dimensionality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Identifying Representative Trends in Massive Time Series Data Sets Using Sketches
VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
Simple analysis of graph tests for linearity and PCP
Random Structures & Algorithms
Periodicity testing with sublinear samples and space
ACM Transactions on Algorithms (TALG)
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Testing permutation properties through subpermutations
Theoretical Computer Science
Hi-index | 0.00 |
A string α∈Σn is called p-periodic, if for every i,j ∈ {1,...,n}, such that $i\equiv j \bmod p$, 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 ε-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 ε-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 ε-testers for period(≤ g) when g varies in the range $1,\dots,\frac{n}{2}$. 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≥ (logn)1+δ, the number of queries required and sufficient for testing period(≤ g) is polynomial in g. On the other hand, for each $g\leq \frac{log{n}}{4}$, the number of queries required and sufficient for testing period(≤ g) is only poly-logarithmic in g. We also prove an exact asymptotic bound for testing general periodicity. Namely, that 1-sided error, non adaptive ε-testing of periodicity ($period(\leq \frac{n}{2})$) is $\Theta(\sqrt{n\log{n}})$ queries.