Streaming Algorithms for Monotonicity Testing

Consider a poset - or equivalently an $n$-vertex DAG $G=(V, E)$ - and a boolean function $f: V \rightarrow \{0, 1\}$ on its vertex set. We say $f$ is monotone if $f(u) \leq f(v)$ for all $(u, v) \in E$. While there is extensive literature on the query complexity of testing monotonicity, we focus ins