Improved direct product theorems for randomized query complexity
نویسندگان
چکیده
منابع مشابه
Direct Product Theorems for Classical Communication Complexity via Subdistribution Bounds
A basic question in complexity theory is whether the computational resources required for solving k independent instances of the same problem scale as k times the resources required for one instance. We investigate this question in various models of classical communication complexity. We introduce a new measure, the subdistribution bound , which is a relaxation of the wellstudied rectangle or c...
متن کاملDirect Product Theorems for Communication Complexity via Subdistribution Bounds
A basic question in complexity theory is whether the computational resources required for solving k independent instances of the same problem scale as k times the resources required for one instance. We investigate this question in various models of classical communication complexity. We define a new measure, the subdistribution bound , which is a generalization of the well-studied rectangle or...
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Let f : {0, 1} → {0, 1} be a Boolean function. The certificate complexity C(f) is a complexity measure that is quadratically tight for the zero-error randomized query complexity R0(f): C(f) ≤ R0(f) ≤ C(f) . In this paper we study a new complexity measure that we call expectational certificate complexity EC(f), which is also a quadratically tight bound on R0(f): EC(f) ≤ R0(f) = O(EC(f) ). We pro...
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Let the randomized query complexity of a relation for error probability ǫ be denoted by Rǫ(·). We prove that for any relation f ⊆ {0, 1} × R and Boolean function g : {0, 1} → {0, 1}, R1/3(f ◦g ) = Ω(R4/9(f) ·R1/2−1/n4(g)), where f ◦g n is the relation obtained by composing f and g. We also show that R1/3 (
متن کاملLifting randomized query complexity to randomized communication complexity
We show that for any (partial) query function f : {0, 1} → {0, 1}, the randomized communication complexity of f composed with Indexm (with m = poly(n)) is at least the randomized query complexity of f times log n. Here Indexm : [m] × {0, 1} → {0, 1} is defined as Indexm(x, y) = yx (the xth bit of y). Our proof follows on the lines of Raz and Mckenzie [RM99] (and its generalization due to [GPW15...
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ژورنال
عنوان ژورنال: computational complexity
سال: 2012
ISSN: 1016-3328,1420-8954
DOI: 10.1007/s00037-012-0043-7