Toward better depth lower bounds: the XOR-KRW conjecture

Ivan Mihajlin, Alexander Smal

Research output: Book/ReportReport


In this paper, we propose a new conjecture, the XOR-KRW conjecture, which is a relaxation of the Karchmer-Raz-Wigderson conjecture [KRW95]. This relaxation is still strong enough to imply PNC1 if proven. We also present a weaker version of this conjecture that might be used for breaking n3 lower bound for De~Morgan formulas. Our study of this conjecture allows us to partially answer an open question stated in [GMWW17] regarding the composition of the universal relation with a function. To be more precise, we prove that there exists a function g such that the composition of the universal relation with g is significantly harder than just a universal relation. The fact that we can only prove the existence of g is an inherent feature of our approach.

The paper's main technical contribution is a method of converting lower bounds for multiplexer-type relations into lower bounds against functions. In order to do this, we develop techniques to lower bound communication complexity using reductions from non-deterministic communication complexity and non-classical models: half-duplex and partially half-duplex communication models.
Original languageAmerican English
StatePublished - 2020


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