eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-02-27
8:1
8:14
10.4230/LIPIcs.STACS.2018.8
article
All Classical Adversary Methods are Equivalent for Total Functions
Ambainis, Andris
Kokainis, Martins
Prusis, Krisjanis
Vihrovs, Jevgenijs
We show that all known classical adversary lower bounds on randomized query complexity are equivalent for total functions, and are equal to the fractional block sensitivity fbs(f). That includes the Kolmogorov complexity bound of Laplante and Magniez and the earlier relational adversary bound of Aaronson. For partial functions, we show unbounded separations between fbs(f) and other adversary bounds, as well as between the relational and Kolmogorov complexity bounds.
We also show that, for partial functions, fractional block sensitivity cannot give lower bounds larger than sqrt(n * bs(f)), where n is the number of variables and bs(f) is the block sensitivity. Then we exhibit a partial function f that matches this upper bound, fbs(f) = Omega(sqrt(n * bs(f))).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol096-stacs2018/LIPIcs.STACS.2018.8/LIPIcs.STACS.2018.8.pdf
Randomized Query Complexity
Lower Bounds
Adversary Bounds
Fractional Block Sensitivity