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A composition theorem for randomized query complexity via Max-conflict complexity
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SYSNO ASEP 0507748 Druh ASEP C - Konferenční příspěvek (mezinárodní konf.) Zařazení RIV D - Článek ve sborníku Název A composition theorem for randomized query complexity via Max-conflict complexity Tvůrce(i) Gavinsky, Dmitry (MU-W) RID, SAI, ORCID
Lee, T. (AU)
Santha, M. (SG)
Sanyal, S. (IN)Číslo článku 64 Zdroj.dok. 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). - Dagstuhl : Schloss Dagstuhl, Leibniz-Zentrum für Informatik, 2019 / Baier Ch. ; Chatzigiannakis I. ; Flocchini P. ; Leonardi S. - ISSN 1868-8969 - ISBN 978-3-95977-109-2 Poč.str. 13 s. Forma vydání Tištěná - P Akce 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) Datum konání 08.07.2019 - 12.07.2019 Místo konání Patras Země GR - Řecko Typ akce WRD Jazyk dok. eng - angličtina Země vyd. DE - Německo Klíč. slova query complexity ; lower bounds Vědní obor RIV IN - Informatika Obor OECD Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) CEP GX19-27871X GA ČR - Grantová agentura ČR Institucionální podpora MU-W - RVO:67985840 EID SCOPUS 85069200872 DOI 10.4230/LIPIcs.ICALP.2019.64 Anotace For any relation f subseteq {0,1}^n x S and any partial Boolean function g:{0,1}^m -> {0,1,*}, we show that R_{1/3}(f o g^n) in Omega(R_{4/9}(f) * sqrt{R_{1/3}(g)}) , where R_epsilon(*) stands for the bounded-error randomized query complexity with error at most epsilon, and f o g^n subseteq ({0,1}^m)^n x S denotes the composition of f with n instances of g. The new composition theorem is optimal, at least, for the general case of relational problems: A relation f_0 and a partial Boolean function g_0 are constructed, such that R_{4/9}(f_0) in Theta(sqrt n), R_{1/3}(g_0)in Theta(n) and R_{1/3}(f_0 o g_0^n) in Theta(n). The theorem is proved via introducing a new complexity measure, max-conflict complexity, denoted by bar{chi}(*). Its investigation shows that bar{chi}(g) in Omega(sqrt{R_{1/3}(g)}) for any partial Boolean function g and R_{1/3}(f o g^n) in Omega(R_{4/9}(f) * bar{chi}(g)) for any relation f, which readily implies the composition statement. It is further shown that bar{chi}(g) is always at least as large as the sabotage complexity of g. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2020
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