
A Composition Theorem via Conflict Complexity
Let (·) stand for the boundederror randomized query complexity. We show...
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The quantum query complexity of composition with a relation
The negative weight adversary method, ADV^±(g), is known to characterize...
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On the randomised query complexity of composition
Let f⊆{0,1}^n×Ξ be a relation and g:{0,1}^m→{0,1,*} be a promise functio...
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A Tight Composition Theorem for the Randomized Query Complexity of Partial Functions
We prove two new results about the randomized query complexity of compos...
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A note on the tight example in On the randomised query complexity of composition
We make two observations regarding a recent tight example for a composit...
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Conflict complexity is lower bounded by block sensitivity
We show conflict complexity of any total boolean function, recently defi...
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Quadratically Tight Relations for Randomized Query Complexity
Let f:{0,1}^n →{0,1} be a Boolean function. The certificate complexity C...
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A composition theorem for randomized query complexity via max conflict complexity
Let R_ϵ(·) stand for the boundederror randomized query complexity with error ϵ > 0. For any relation f ⊆{0,1}^n × S and partial Boolean function g ⊆{0,1}^m ×{0,1}, we show that R_1/3(f ∘ g^n) ∈Ω(R_4/9(f) ·√(R_1/3(g))), where f ∘ g^n ⊆ ({0,1}^m)^n × S is the composition of f and g. We give an example of a relation f and partial Boolean function g for which this lower bound is tight. We prove our composition theorem by introducing a new complexity measure, the max conflict complexity χ̅(g) of a partial Boolean function g. We show χ̅(g) ∈Ω(√(R_1/3(g))) for any (partial) function g and R_1/3(f ∘ g^n) ∈Ω(R_4/9(f) ·χ̅(g)); these two bounds imply our composition result. We further show that χ̅(g) is always at least as large as the sabotage complexity of g, introduced by BenDavid and Kothari.
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