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 AC⁰ 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. 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.
@InProceedings{bogdanov_et_al:LIPIcs.FSTTCS.2023.23, author = {Bogdanov, Andrej and Dinesh, Krishnamoorthy and Filmus, Yuval and Ishai, Yuval and Kaplan, Avi and Sekar, Sruthi}, title = {{Bounded Simultaneous Messages}}, booktitle = {43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)}, pages = {23:1--23:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-304-1}, ISSN = {1868-8969}, year = {2023}, volume = {284}, editor = {Bouyer, Patricia and Srinivasan, Srikanth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.23}, URN = {urn:nbn:de:0030-drops-193961}, doi = {10.4230/LIPIcs.FSTTCS.2023.23}, annote = {Keywords: Simultaneous Messages, Instance Hiding, Algebraic degree, Preprocessing, Lower Bounds} }
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