A Lower Bound on the Complexity of Testing Grained Distributions

Oded Goldreich; Dana Ron

doi:10.1007/s00037-023-00245-w

A Lower Bound on the Complexity of Testing Grained Distributions

Oded Goldreich, Dana Ron

Weizmann Institute of Science, Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

For a natural number m , a distribution is called m -grained, if each element appears with probability that is an integer multiple of 1 / m . We prove that, for any constant c< 1 , testing whether a distribution over [Θ (m)] is m -grained requires Ω (m^c) samples, where testing a property of distributions means distinguishing between distributions that have the property and distributions that are far (in total variation distance) from any distribution that has the property.

Original language	English
Article number	11
Number of pages	16
Journal	Computational Complexity
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/s00037-023-00245-w
State	Published - Dec 2023

Keywords

68Q25
Property testing
distributions

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Mathematics
Computational Theory and Mathematics
Computational Mathematics

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10.1007/s00037-023-00245-w

Cite this

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A Lower Bound on the Complexity of Testing Grained Distributions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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