Depth Tradeoffs for Clique and Connectivity


Ben Rossman October 6, 2023.


This talk will give an overview of size-depth tradeoffs for the important k-CLIQUE and DISTANCE-k CONNECTIVITY problems. In particular, I will discuss recent lower bounds for AC0 circuits and formulas that were obtained – via a novel “lifting” technique – from tradeoffs in the parameters of simpler combinatorial objects (e.g. subgraph coverings of the order-k path graph). In the talk, I will explain the underlying combinatorial tradeoffs; say a few words about lifting technique; and discuss the big-picture questions of P vs NP and NC1 vs L that motivate this work.

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