Search Results - Randomized query complexity

The randomized query complexity of finding a Tarski fixed point on the Boolean hypercube by Brânzei, Simina, Phillips, Reed, Recker, Nicholas

“…—the original setting of the Knaster-Tarski theorem. We prove a lower bound that characterizes the randomized and deterministic query complexity of the Tarski search problem on the Boolean hypercube as Θ(k…”
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Quadratically Tight Relations for Randomized Query Complexity by Jain, Rahul, Klauck, Hartmut, Kundu, Srijita, Lee, Troy, Santha, Miklos, Sanyal, Swagato, Vihrovs, Jevgēnijs

“…In this work we investigate the problem of quadratically tightly approximating the randomized query complexity of Boolean functions R ( f…”
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Towards Optimal Separations between Quantum and Randomized Query Complexities by Tal, Avishay

“… To date, separations of O(1) vs. \sqrt{N} between quantum and randomized query complexities remain the state-of-the-art…”
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A Tight Composition Theorem for the Randomized Query Complexity of Partial Functions: Extended Abstract by Ben-David, Shalev, Blais, Eric

“…We prove two new results about the randomized query complexity of composed functions…”
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Improved direct product theorems for randomized query complexity by Drucker, Andrew

“… . We prove the following direct product theorem (DPT) for query complexity: if every T -query algorithm has success probability at most in computing the Boolean function f on input distribution  μ , then for α…”
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Lifting randomized query complexity to randomized communication complexity by Anshu, Anurag, Goud, Naresh B, Jain, Rahul, Kundu, Srijita, Mukhopadhyay, Priyanka

“…\) under the uniform distribution and \(\mathrm{R}_{1/3}(f)\) (\(\mathrm{R}_{1/3}(f\circ g^n)\)) denotes the randomized query complexity of \(f…”
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Improved Direct Product Theorems for Randomized Query Complexity by Drucker, A.

“… We prove the following direct product theorem (DPT) for query complexity: if every T-query algorithm has success probability at most 1 - ε…”
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Optimal Separation and Strong Direct Sum for Randomized Query Complexity by Blais, Eric, Brody, Joshua

“…We establish two results regarding the query complexity of bounded-error randomized algorithms…”
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On the Composition of Randomized Query Complexity and Approximate Degree by Chakraborty, Sourav, Kayal, Chandrima, Mittal, Rajat, Paraashar, Manaswi, Sanyal, Swagato, Saurabh, Nitin

“…For any Boolean functions \(f\) and \(g\), the question whether \(R(f\circ g) = \tilde{\Theta}(R(f)R(g))\), is known as the composition question for the randomized query complexity…”
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Lower Bounds for Randomized and Quantum Query Complexity Using Kolmogorov Arguments by Laplante, Sophie, Magniez, Frédéric

“…We prove a very general lower bound technique for quantum and randomized query complexity that is easy to prove as well as to apply…”
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Randomized query complexity of sabotaged and composed functions by Ben-David, Shalev, Kothari, Robin

“…We study the composition question for bounded-error randomized query complexity: Is R(f o g) = Omega(R(f) R(g)) for all Boolean functions f and g…”
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A Strong XOR Lemma for Randomized Query Complexity by Brody, Joshua, Kim, Jae Tak, Lerdputtipongporn, Peem, Hariharan Srinivasulu

“…\), the randomized query complexity of computing the xor of k instances of g satisfies \(\overline{R}_\eps(xor\circ g) = \Theta(k \overline{R}_{\eps/k}(g))\). This matches…”
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When Is Amplification Necessary for Composition in Randomized Query Complexity? by Ben-David, Shalev, Göös, Mika, Kothari, Robin, Watson, Thomas

“…Suppose we have randomized decision trees for an outer function \(f\) and an inner function \(g…”
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Unambiguous Parity‐Query Complexity by Gavinsky, Dmytro

“…‐query complexity of the approximate majority problem—that is, on the lowest randomized parity…”
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Quadratically Tight Relations for Randomized Query Complexity by Gavinsky, Dmitry, Jain, Rahul, Klauck, Hartmut, Kundu, Srijita, Lee, Troy, Santha, Miklos, Sanyal, Swagato, Vihrovs, Jevgenijs

“…)\) is a complexity measure that is quadratically tight for the zero-error randomized query complexity \(R_0(f)\): \(C(f) \leq R_0(f) \leq C(f)^2…”
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A Composition Theorem for Randomized Query Complexity by Anshu, Anurag, Gavinsky, Dmitry, Jain, Rahul, Kundu, Srijita, Lee, Troy, Mukhopadhyay, Priyanka, Santha, Miklos, Sanyal, Swagato

“…Let the randomized query complexity of a relation for error probability \(\epsilon\) be denoted by \(R_\epsilon(\cdot)\). We prove that for any…”
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A Tight Composition Theorem for the Randomized Query Complexity of Partial Functions by Ben-David, Shalev, Blais, Eric

“…We prove two new results about the randomized query complexity of composed functions…”
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Towards Optimal Separations between Quantum and Randomized Query Complexities by Tal, Avishay

“… To date, separations of \(O(1)\) vs. \(\sqrt{N}\) between quantum and randomized query complexities remain the state-of-the-art (where \(N…”
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A New Minimax Theorem for Randomized Algorithms (Extended Abstract) by Ben-David, Shalev, Blais, Eric

“…The celebrated minimax principle of Yao (1977) says that for any Boolean-valued function f with finite domain, there is a distribution \mu over the domain of f…”
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A composition theorem for randomized query complexity via max conflict complexity by Gavinsky, Dmitry, Lee, Troy, Santha, Miklos, Sanyal, Swagato

“…Let \(R_\epsilon(\cdot)\) stand for the bounded-error randomized query complexity with error \(\epsilon > 0\). For any relation \(f \subseteq \{0,1\}^n \times…”
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