Gilbert Théodore Maystre

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The unifying theme of this thesis are decision trees. Given a boolean function

f

and an input

x

, a decision tree computes the value

f(x)

by repeatedly querying bits of

x

. Our work is two-fold. On one hand, we investigate direct sums and other relat ...

Simon (1998) proved that it is impossible to construct collision-resistant hash functions from one-way functions using a black-box reduction. It is conjectured more generally that one-way functions do not imply, via a black-box reduction, the hardness of a ...

We show EOPL = PLS \cap PsansP \sansP AD. Here the class EOPL consists of all total search problems that reduce to the END -OF -POTENTIAL -LINE problem, which was introduced in the works by Hub'acv \ek and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 202 ...

Aaronson (STOC 2010) conjectured that almost k-wise independence fools constant-depth circuits; he called this the generalised Linial-Nisan conjecture. Aaronson himself later found a counterexample for depth-3 circuits. We give here an improved counterexam ...

We show that computing the majority of n copies of a boolean function g has randomised query complexity R(Maj∘gⁿ) = Θ(n⋅R ̅_{1/n}(g)). In fact, we show that to obtain a similar result for any composed function f∘gⁿ, it suffices to prove a sufficiently stro ...

We exhibit a monotone function computable by a monotone circuit of quasipolynomial size such that any monotone circuit of polynomial depth requires exponential size. This is the first size–depth tradeoff result for monotone circuits in the so-called superc ...

Direct sum theorems state that the cost of solving k instances of a problem is at least Ω(k) times the cost of solving a single instance. We prove the first such results in the randomised parity decision tree model. We show that a direct sum theorem holds ...

We show EOPL = PLS ∩ PPAD. Here the class EOPL consists of all total search problems that reduce to the End-of-Potential-Line problem, which was introduced in the works by Hubáček and Yogev (SICOMP 2020) and Fearnley et al. (JCSS 2020). In particular, our ...

Gilbert Théodore Maystre

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The Power of Decision Trees for Composition and Search Problems

One-Way Functions vs. TFNP: Simpler and Improved

Further Collapses in TFNP

Generalised Linial-Nisan Conjecture Is False for DNFs

A Majority Lemma for Randomised Query Complexity

Supercritical Tradeoffs for Monotone Circuits

Separations in Proof Complexity and TFNP

Randomised Composition and Small-Bias Minimax

Direct Sums for Parity Decision Trees

Further Collapses in TFNP