All reports by Author Gilbert Maystre:

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TR22-112
| 12th August 2022
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Shalev Ben-David, Eric Blais, Mika Göös, Gilbert Maystre#### Randomised Composition and Small-Bias Minimax

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TR22-058
| 26th April 2022
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Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, Ran Tao#### Separations in Proof Complexity and TFNP

Revisions: 1

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TR22-018
| 15th February 2022
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Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, Ran Tao#### Further Collapses in TFNP

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TR21-024
| 15th February 2021
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Mika Göös, Gilbert Maystre#### A Majority Lemma for Randomised Query Complexity

Shalev Ben-David, Eric Blais, Mika Göös, Gilbert Maystre

We prove two results about randomised query complexity $\mathrm{R}(f)$. First, we introduce a linearised complexity measure $\mathrm{LR}$ and show that it satisfies an inner-optimal composition theorem: $\mathrm{R}(f\circ g) \geq \Omega(\mathrm{R}(f) \mathrm{LR}(g))$ for all partial $f$ and $g$, and moreover, $\mathrm{LR}$ is the largest possible measure with this property. In particular, ... more >>>

Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, Ran Tao

It is well-known that Resolution proofs can be efficiently simulated by Sherali-Adams (SA) proofs. We show, however, that any such simulation needs to exploit huge coefficients: Resolution cannot be efficiently simulated by SA when the coefficients are written in unary. We also show that Reversible Resolution (a variant of MaxSAT ... more >>>

Mika Göös, Alexandros Hollender, Siddhartha Jain, Gilbert Maystre, William Pires, Robert Robere, Ran Tao

We show $\text{EOPL}=\text{PLS}\cap\text{PPAD}$. Here the class $\text{EOPL}$ consists of all total search problems that reduce to the End-of-Potential-Line problem, which was introduced in the works by Hubacek and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 2020). In particular, our result yields a new simpler proof of the breakthrough collapse ... more >>>

Mika Göös, Gilbert Maystre

We show that computing the majority of $n$ copies of a boolean function $g$ has randomised query complexity $\mathrm{R}(\mathrm{Maj} \circ g^n) = \Theta(n\cdot \bar{\mathrm{R}}_{1/n}(g))$. In fact, we show that to obtain a similar result for any composed function $f\circ g^n$, it suffices to prove a sufficiently strong form of the ... more >>>