Roksana Baleshzar

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We study the problem of testing unateness of functions f : {0, 1}d → R.We give aO( ε ·log d ε )query nonadaptive tester and a O( ε )-query adaptive tester and show that both testers are optimal for a fixed distance parameter ε. Previously known unateness testers worked only for Boolean functions, and their query complexity had worse dependence on the(More)
We give a unateness tester for functions of the form f : [n] → R, where n, d ∈ N and R ⊆ R with query complexity O( log(max(d,n)) ). Previously known unateness testers work only for Boolean functions over the domain {0, 1}. We show that every unateness tester for realvalued functions over hypergrid has query complexity Ω(min{d, |R|}). Consequently, our(More)
A Boolean function f : {0, 1} 7→ {0, 1} is unate if, along each coordinate, the function is either nondecreasing or nonincreasing. In this note, we prove that any nonadaptive, one-sided error unateness tester must make Ω( d log d ) queries. This result improves upon the Ω( d log2 d ) lower bound for the same class of testers due to Chen et al. (STOC, 2017).
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