All reports by Author Akash Kumar:

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TR17-088
| 10th May 2017
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Elena Grigorescu, Akash Kumar, Karl Wimmer#### K-Monotonicity is Not Testable on the Hypercube

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TR16-136
| 31st August 2016
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Clement Canonne, Elena Grigorescu, Siyao Guo, Akash Kumar, Karl Wimmer#### Testing k-Monotonicity

Revisions: 1

Elena Grigorescu, Akash Kumar, Karl Wimmer

We continue the study of $k$-monotone Boolean functions in the property testing model, initiated by Canonne et al. (ITCS 2017). A function $f:\{0,1\}^n\rightarrow \{0,1\}$ is said to be $k$-monotone if it alternates between $0$ and $1$ at most $k$ times on every ascending chain. Such functions represent a natural generalization ... more >>>

Clement Canonne, Elena Grigorescu, Siyao Guo, Akash Kumar, Karl Wimmer

A Boolean $k$-monotone function defined over a finite poset domain ${\cal D}$ alternates between the values $0$ and $1$ at most $k$ times on any ascending chain in ${\cal D}$. Therefore, $k$-monotone functions are natural generalizations of the classical monotone functions, which are the $1$-monotone functions.

Motivated by the ... more >>>