# Editing Open Problems:70

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{{Header | {{Header | ||

+ | |title=Open Problems in $L_p$-Testing | ||

|source=baltimore16 | |source=baltimore16 | ||

|who=Grigory Yaroslavtsev | |who=Grigory Yaroslavtsev | ||

}} | }} | ||

+ | |||

Extending the usual setting of property testing to functions $f\colon\{1,\dots,n\}^d\to[0,1]$, Berman et al. {{cite|BermanRY-14}} study property testing with regard to $L_p$ distances between functions. Namely, these distances are defined as $\operatorname{dist}_p(f,g) = \frac{\lVert f-g\rVert_p}{\lVert \mathbf{1}\rVert_p}$ (for $p > 0$), so that for instance $\operatorname{dist}_1(f,g) = \frac{\lVert f-g\rVert_1}{n^d}$ (and if the functions are Boolean, we get back the Hamming distance). | Extending the usual setting of property testing to functions $f\colon\{1,\dots,n\}^d\to[0,1]$, Berman et al. {{cite|BermanRY-14}} study property testing with regard to $L_p$ distances between functions. Namely, these distances are defined as $\operatorname{dist}_p(f,g) = \frac{\lVert f-g\rVert_p}{\lVert \mathbf{1}\rVert_p}$ (for $p > 0$), so that for instance $\operatorname{dist}_1(f,g) = \frac{\lVert f-g\rVert_1}{n^d}$ (and if the functions are Boolean, we get back the Hamming distance). | ||