We continue the study of half-duplex communication complexity, a model introduced in [HIMS18] and further studied in [DISSU21], in which each player can either send a bit or listen in each round, similarly to communication over a walkie-talkie.
We prove improved upper bounds for the Inner Product function in the half-duplex models with silence and with zero, as well as an improved upper bound for the Disjointness function in the model with zero.
We also determine the half-duplex communication complexity of a uniformly random Boolean function up to an additive constant: with high probability, it is $n/\log_2 3 + O(1)$ in the model with silence and $n + O(1)$ in the models with zero and with an adversary.