Kumar (CCC, 2023) used a novel switching lemma to prove exponential-size lower bounds for a circuit class $GC^0$ that not only contains $AC^0$ but can---with a single gate---compute functions that require exponential-size $TC^0$ circuits. Their main result was that switching-lemma lower bounds for $AC^0$ lift to $GC^0$ with no loss ... more >>>

We propose a framework of algorithm vs. hardness for all Max-CSPs and demonstrate it for a large class of predicates. This framework extends the work of Raghavendra [STOC, 2008], who showed a similar result for almost satisfiable Max-CSPs.

Our framework is based on a new hybrid approximation algorithm, which uses ... more >>>

The propositional proof system resolution over parities (Res($\oplus$)) combines resolution and the linear algebra over GF(2). It is a challenging open question to prove a superpolynomial lower bound on the proof size in this system. For many years, superpolynomial lower bounds were known only in tree-like cases. Recently, Efremenko, Garlik, ... more >>>