This work studies the fundamental search problem of\textsc{element-extraction} in a query model that combines both: linearmeasurements with bounded adaptivity . In the problem, one is given a nonzero vector$\mathbf{z} = (z_1,\ldots,z_n) and must report an index $i$where $z_i = 1$. This problem admits an efficient nonadaptiverandomized solution (through the well known technique of $ell_0$-sampling) and an efficient fully adaptive deterministic solution . Weprove that when confined to only $k$ rounds of adaptivity, a deterministic . algorithm must spend $Omega(k (n = 1/k)$queries, when working in the ring of integers modulo some fixed $q$. Thismatches the corresponding upper bound. For queries using integer arithmetic, weprove a $2$-round

Author(s) : Amit Chakrabarti, Manuel Stoeckl

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Keywords : problem - adaptivity - z - queries - deterministic -

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