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Krw composition theorems via lifting
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SYSNO ASEP 0539556 Druh ASEP C - Konferenční příspěvek (mezinárodní konf.) Zařazení RIV D - Článek ve sborníku Název Krw composition theorems via lifting Tvůrce(i) de Rezende, Susanna F. (MU-W) ORCID, SAI, RID
Meir, O. (IL)
Norström, J. (SE)
Pitassi, T. (US)
Robere, R. (CA)Zdroj.dok. 2020 IEEE 61st Annual Symposium on Foundations of Computer Science. - Los Alamitos : IEEE, 2020 - ISBN 978-1-7281-9622-0 Rozsah stran s. 43-49 Poč.str. 7 s. Forma vydání Tištěná - P Akce 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020 Datum konání 16.11.2020 - 19.11.2020 Místo konání Durham Země US - Spojené státy americké Typ akce WRD Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova circuit complexity ; circuit lower bounds ; communication complexity Vědní obor RIV IN - Informatika Obor OECD Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Institucionální podpora MU-W - RVO:67985840 UT WOS 000652333400005 EID SCOPUS 85100337778 DOI 10.1109/FOCS46700.2020.00013 Anotace One of the major open problems in complexity theory is proving super-logarithmic lower bounds on the depth of circuits (i.e., mathrm{P} nsubseteq text{NC}{1}). Karchmer, Raz, and Wigderson [13] suggested to approach this problem by proving that depth complexity behaves'as expected' with respect to the composition of functions f diamond g. They showed that the validity of this conjecture would imply that mathrm{P} nsubseteq text{NC}{1}. Several works have made progress toward resolving this conjecture by proving special cases. In particular, these works proved the KRW conjecture for every outer function, but only for few inner functions. Thus, it is an important challenge to prove the KRW conjecture for a wider range of inner functions. In this work, we extend significantly the range of inner functions that can be handled. First, we consider the monotone version of the KRW conjecture. We prove it for every monotone inner function whose depth complexity can be lower bounded via a query-to-communication lifting theorem. This allows us to handle several new and well-studied functions such as the s-t-connectivity, clique, and generation functions. In order to carry this progress back to the non-monotone setting, we introduce a new notion of semi-monotone composition, which combines the non-monotone complexity of the outer function with the monotone complexity of the inner function. In this setting, we prove the KRW conjecture for a similar selection of inner functions, but only for a specific choice of the outer function f. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2021
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