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Publications [#348683] of Benjamin Rossman

Papers Published

  1. Kawachi, A; Rossman, B; Watanabe, O, The query complexity of witness finding, Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8476 LNCS (January, 2014), pp. 218-231, ISBN 9783319066851 [doi]
    (last updated on 2022/05/21)

    We study the following information-theoretic witness finding problem: for a hidden nonempty subset W of {0,1} n, how many non-adaptive randomized queries (yes/no questions about W) are needed to guess an element x∈ {0,1} n such that x∈ W with probability >∈1/2? Motivated by questions in complexity theory, we prove tight lower bounds with respect to a few different classes of queries: We show that the monotone query complexity of witness finding is Ω(n 2). This matches an O(n 2) upper bound from the Valiant-Vazirani Isolation Lemma [8]. We also prove a tight Ω(n 2) lower bound for the class of NP queries (queries defined by an NP machine with an oracle to W). This shows that the classic search-to-decision reduction of Ben-David, Chor, Goldreich and Luby [3] is optimal in a certain black-box model. Finally, we consider the setting where W is an affine subspace of {0,1} n and prove an Ω(n 2) lower bound for the class of intersection queries (queries of the form "W∈∈S∈∈ ?" where S is a fixed subset of {0,1} n ). Along the way, we show that every monotone property defined by an intersection query has an exponentially sharp threshold in the lattice of affine subspaces of {0,1} n . © 2014 Springer International Publishing Switzerland.
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