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Separation Between Deterministic and Randomized Query Complexity
KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
Tata Inst Fundamental Res, Bombay, Maharashtra, India..
IIT Kharagpur, Dept Comp Sci & Engn, Kharagpur, W Bengal, India..
2018 (English)In: SIAM journal on computing (Print), ISSN 0097-5397, E-ISSN 1095-7111, Vol. 47, no 4, p. 1644-1666Article in journal (Refereed) Published
Abstract [en]

Saks and Wigderson 27th FOGS, IEEE Computer Society, as Alamitos, CA, 1986, pp. 29-38] conjectured that R-0(f) = Omega (D(f)(0.753...)) for all Boolean functions f, here R-0 denotes the randomized complexity and D denotes 10 determinist is query CCATI p1exit;,yr. We,show t hat for the pointer function GPW(rxs) defined by Goos. Pitassi, arid Watson [in Proceedings of the 56th FOCS, IEEE, Piscataway, NJ, 2015, pp. 1077-1088] the following hold: s) s) and (b) R-1(GPW(rxs)) = Irs), cyhere R1 denotes the randomized one-sided error query complexity. These results imply that (i) R-0(GPW(s2xs)) = O(D(GPW(s2xs))2/3) t hereby refuting the; conjecture of Saks and Wigdorson, and (ii) R-1 (GPW(sxs))- O(R-0(GPW(sxs))(2/3)), thereby providing a polynomial separation between the randomized zero -error and one-sided error query complexity measures.

Place, publisher, year, edition, pages
Siam Publications , 2018. Vol. 47, no 4, p. 1644-1666
Keywords [en]
deterministic decision tree, randomized decision tree, query complexity, models of computation
National Category
Computer Sciences Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-235160DOI: 10.1137/17M1124115ISI: 000443195600013Scopus ID: 2-s2.0-85053616543OAI: oai:DiVA.org:kth-235160DiVA, id: diva2:1249349
Note

QC 20180919

Available from: 2018-09-19 Created: 2018-09-19 Last updated: 2018-10-16Bibliographically approved

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