A frontier open problem in circuit complexity is to prove P^{NP} is not in SIZE [n^ k] for all k;
this is a necessary intermediate step towards NP is not in P_ {/poly}. Previously, for several …

A fundamental question in computational complexity asks whether probabilistic polynomial-
time algorithms can be simulated deterministically with a small overhead in time (the BPP vs …

In several settings, derandomization is known to follow from circuit lower bounds that
themselves are equivalent to the existence of pseudorandom generators. This leaves open …

In this work we study oblivious complexity classes. These classes capture the power of
interactive proofs where the prover (s) are only given the input size rather than the actual …

Most of the known lower bounds for binary Boolean circuits with unrestricted depth are
proved by the gate elimination method. The most efficient known algorithms for the# SAT …

Many derandomization results for probabilistic decision processes have been ported to the
setting of Arthur-Merlin protocols. Whereas the ultimate goal in the first setting consists of …

The subfield of derandomization in computational complexity theory aims to understand the
conditions under which randomness can be efficiently reduced or completely eliminated …

Most of the known lower bounds for binary Boolean circuits with unrestricted depth are
proved by the gate elimination method. The most efficient known algorithms for the# SAT …

While Complexity Theory has been centered around several major open problems about the
relationships between complexity classes, showing resource lower bounds which amount to …

What is the role of randomness in computation? This thesis focuses on the prBPP= prP
conjecture, which asserts that randomness is not crucial for efficiently solving decision …