Bounded simultaneous messages

Andrej Bogdanov, Krishnamoorthy Dinesh, Yuval Filmus, Yuval Ishai, Avi Kaplan, Sruthi Sekar

We consider the following question of bounded simultaneous messages (BSM) protocols: Can computationally unbounded Alice and Bob evaluate a function $f(x,y)$ of their inputs by sending polynomial-size messages to a computationally bounded Carol? The special case where $f$ is the mod-2 inner-product function and Carol is bounded to $\mathsf{AC}^0$ has been studied in previous works. The general question can be broadly motivated by applications in which distributed computation is more costly than local computation, including secure two-party computation.

In this work, we initiate a more systematic study of the BSM model, with different functions $f$ and computational bounds on Carol. In particular, we give evidence against the existence of BSM protocols with polynomial-size Carol for naturally distributed variants of NP-complete languages.


  title = {Bounded simultaneous messages},
  author = {Andrej Bogdanov and Krishnamoorthy Dinesh and Yuval Filmus and Yuval Ishai and Avi Kaplan and Sruthi Sekar},
  booktitle = {FSTTCS'23},
  year = {2023},
  pages = {23:1--23:17},
  doi = {10.4230/LIPIcs.FSTTCS.2023.23}
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