For any fixed $t$, we present two fine-grained reductions of the problem of approximately counting the number of $t$-cliques in a graph to the problem of detecting a $t$-clique in a graph.
One of our reductions is slightly better than the prior reduction of Dell, Lapinskas, and Meeks (SODA20) and ... more >>>

Boolean function $F(x,y)$ for $x,y \in \{0,1\}^n$ is an XOR function if $F(x,y) = f(x\oplus y)$ for some function $f$ on $n$ input bits, where $\oplus$ is a bit-wise XOR. XOR functions are relevant in communication complexity, partially for allowing Fourier analytic technique. For total XOR functions it is known ... more >>>

In a recent breakthrough, Chen, Hirahara and Ren prove that S$_2$E/$_1 \not\subset$ SIZE$[2^n/n]$ by giving a single-valued FS$_2$P algorithm for the Range Avoidance Problem (Avoid) that works for infinitely many input size $n$.

Building on their work, we present a simple single-valued FS$_2$P algorithm for Avoid that works for all ... more >>>