Testing Unateness of Real-Valued Functions
We give a unateness tester for functions of the form $f:[n]^d\rightarrow R$, where $n,d\in \mathbb{N}$ and $R\subseteq \mathbb{R}$ with query complexity $O(\frac{d\log (\max(d,n))}{\epsilon})$. Previously known unateness testers work only for Boolean functions over the domain $\{0,1\}^d$. We show th...
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| creator | Baleshzar, Roksana Murzabulatov, Meiram Pallavoor, Ramesh Krishnan S Raskhodnikova, Sofya |
| description | We give a unateness tester for functions of the form $f:[n]^d\rightarrow R$,
where $n,d\in \mathbb{N}$ and $R\subseteq \mathbb{R}$ with query complexity
$O(\frac{d\log (\max(d,n))}{\epsilon})$. Previously known unateness testers
work only for Boolean functions over the domain $\{0,1\}^d$. We show that every
unateness tester for real-valued functions over hypergrid has query complexity
$\Omega(\min\{d, |R|^2\})$. Consequently, our tester is nearly optimal for
real-valued functions over $\{0,1\}^d$. We also prove that every nonadaptive,
1-sided error unateness tester for Boolean functions needs
$\Omega(\sqrt{d}/\epsilon)$ queries. Previously, no lower bounds for testing
unateness were known. |
| doi_str_mv | 10.48550/arxiv.1608.07652 |
| format | Article |
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where $n,d\in \mathbb{N}$ and $R\subseteq \mathbb{R}$ with query complexity
$O(\frac{d\log (\max(d,n))}{\epsilon})$. Previously known unateness testers
work only for Boolean functions over the domain $\{0,1\}^d$. We show that every
unateness tester for real-valued functions over hypergrid has query complexity
$\Omega(\min\{d, |R|^2\})$. Consequently, our tester is nearly optimal for
real-valued functions over $\{0,1\}^d$. We also prove that every nonadaptive,
1-sided error unateness tester for Boolean functions needs
$\Omega(\sqrt{d}/\epsilon)$ queries. Previously, no lower bounds for testing
unateness were known.</description><identifier>DOI: 10.48550/arxiv.1608.07652</identifier><language>eng</language><subject>Computer Science - Data Structures and Algorithms</subject><creationdate>2016-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1608.07652$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1608.07652$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Baleshzar, Roksana</creatorcontrib><creatorcontrib>Murzabulatov, Meiram</creatorcontrib><creatorcontrib>Pallavoor, Ramesh Krishnan S</creatorcontrib><creatorcontrib>Raskhodnikova, Sofya</creatorcontrib><title>Testing Unateness of Real-Valued Functions</title><description>We give a unateness tester for functions of the form $f:[n]^d\rightarrow R$,
where $n,d\in \mathbb{N}$ and $R\subseteq \mathbb{R}$ with query complexity
$O(\frac{d\log (\max(d,n))}{\epsilon})$. Previously known unateness testers
work only for Boolean functions over the domain $\{0,1\}^d$. We show that every
unateness tester for real-valued functions over hypergrid has query complexity
$\Omega(\min\{d, |R|^2\})$. Consequently, our tester is nearly optimal for
real-valued functions over $\{0,1\}^d$. We also prove that every nonadaptive,
1-sided error unateness tester for Boolean functions needs
$\Omega(\sqrt{d}/\epsilon)$ queries. Previously, no lower bounds for testing
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where $n,d\in \mathbb{N}$ and $R\subseteq \mathbb{R}$ with query complexity
$O(\frac{d\log (\max(d,n))}{\epsilon})$. Previously known unateness testers
work only for Boolean functions over the domain $\{0,1\}^d$. We show that every
unateness tester for real-valued functions over hypergrid has query complexity
$\Omega(\min\{d, |R|^2\})$. Consequently, our tester is nearly optimal for
real-valued functions over $\{0,1\}^d$. We also prove that every nonadaptive,
1-sided error unateness tester for Boolean functions needs
$\Omega(\sqrt{d}/\epsilon)$ queries. Previously, no lower bounds for testing
unateness were known.</abstract><doi>10.48550/arxiv.1608.07652</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Data Structures and Algorithms |
| title | Testing Unateness of Real-Valued Functions |
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