  Motivated by recent works on streaming algorithms for constraint satisfaction
problems (CSPs), we define and analyze oblivious algorithms for the Max-$k$AND
problem. This generalizes the definition by Feige and Jozeph (Algorithmica '15)
of oblivious algorithms for Max-DICUT, a special case of Max-$2$AND. Oblivious
algorithms round each variable with probability depending only on a quantity
called the variable's bias.
  For each oblivious algorithm, we design a so-called "factor-revealing linear
program" (LP) which captures its worst-case instance, generalizing one of Feige
and Jozeph for Max-DICUT. Then, departing from their work, we perform a fully
explicit analysis of these (infinitely many!) LPs. In particular, we show that
for all $k$, oblivious algorithms for Max-$k$AND provably outperform a special
subclass of algorithms we call "superoblivious" algorithms.
  Our result has implications for streaming algorithms: Generalizing the result
for Max-DICUT of Saxena, Singer, Sudan, and Velusamy (SODA'23), we prove that
certain separation results hold between streaming models for infinitely many
CSPs: for every $k$, $O(\log n)$-space sketching algorithms for Max-$k$AND
known to be optimal in $o(\sqrt n)$-space can be beaten in (a) $O(\log
n)$-space under a random-ordering assumption, and (b) $O(n^{1-1/k} D^{1/k})$
space under a maximum-degree-$D$ assumption. Even in the previously-known case
of Max-DICUT, our analytic proof gives a fuller, computer-free picture of these
separation results.
