We formalize AI alignment as a multi-objective optimization problem called $\langle M,N,\varepsilon,\delta\rangle$-agreement, in which a set of $N$ agents (including humans) must reach approximate ($\varepsilon$) agreement across $M$ candidate objectives, with probability at least $1-\delta$.
Analyzing communication complexity, we prove an information-theoretic lower bound showing that once either $M$ or ... more >>>

We initiate a systematic study of the computational complexity of property testing, focusing on the relationship between query and time complexity. While traditional work in property testing has emphasized query complexity—often via information-theoretic techniques—relatively little is known about the computational hardness of property testers. Our goal is to chart the ... more >>>

The *algebrization barrier*, proposed by Aaronson and Wigderson (STOC '08, ToCT '09), captures the limitations of many complexity-theoretic techniques based on arithmetization. Notably, several circuit lower bounds that overcome the relativization barrier (Buhrman--Fortnow--Thierauf, CCC '98; Vinodchandran, TCS '05; Santhanam, STOC '07, SICOMP '09) remain subject to the algebrization barrier.

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