The log-rank conjecture is a longstanding open problem with multiple equivalent formulations in complexity theory and mathematics. In its linear-algebraic form, it asserts that the rank and partitioning number of a Boolean matrix are quasi-polynomially related.

We propose a relaxed but still equivalent version of the conjecture based on a ... more >>>

Given algorithms $A_1,A_2$ running in logspace and linear time, there are two basic ways to compute the composition $x\rightarrow A_2(A_1(x))$. Applying naive composition gives an algorithm in linear time but linear space, while applying emulative composition (i.e. the composition of space-bounded algorithms) gives an algorithm in logarithmic space but quadratic ... more >>>

A random local function defined by a $d$-ary predicate $P$ is one where each output bit is computed by applying $P$ to $d$ randomly chosen bits of its input. These represent natural distributions of instances for constraint satisfaction problems. They were put forward by Goldreich as candidates for low-complexity one-way ... more >>>